| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 3.1-a1 |
3.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 3^{14} \) |
$1.85575$ |
$(454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.170819533$ |
$7.701729881$ |
2.334447830 |
\( \frac{1295029}{2187} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -2461929 a + 20655252\) , \( -8180265489 a + 68631338793\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2461929a+20655252\right){x}-8180265489a+68631338793$ |
| 3.1-b1 |
3.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 3^{14} \) |
$1.85575$ |
$(454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.170819533$ |
$7.701729881$ |
2.334447830 |
\( \frac{1295029}{2187} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 2461928 a + 18193324\) , \( 8180265488 a + 60451073305\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2461928a+18193324\right){x}+8180265488a+60451073305$ |
| 4.1-a1 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.543135817$ |
$13.68783852$ |
3.769065024 |
\( -\frac{34191163052375}{262144} a - \frac{126334003752875}{131072} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -6743608 a + 56577969\) , \( -40609623585 a + 340709337488\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-6743608a+56577969\right){x}-40609623585a+340709337488$ |
| 4.1-a2 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.629407451$ |
$13.68783852$ |
3.769065024 |
\( -\frac{42875}{64} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 790527 a - 6632421\) , \( 2033260062 a - 17058781354\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(790527a-6632421\right){x}+2033260062a-17058781354$ |
| 4.1-a3 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$4.888222354$ |
$1.520870947$ |
3.769065024 |
\( \frac{34191163052375}{262144} a - \frac{286859170558125}{262144} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 78794542 a - 661075726\) , \( 1069411885670 a - 8972223402422\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(78794542a-661075726\right){x}+1069411885670a-8972223402422$ |
| 4.1-b1 |
4.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$4.888222354$ |
$1.520870947$ |
3.769065024 |
\( -\frac{34191163052375}{262144} a - \frac{126334003752875}{131072} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -78794543 a - 582281183\) , \( -1069411885671 a - 7902811516751\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-78794543a-582281183\right){x}-1069411885671a-7902811516751$ |
| 4.1-b2 |
4.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.629407451$ |
$13.68783852$ |
3.769065024 |
\( -\frac{42875}{64} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -790528 a - 5841893\) , \( -2033260063 a - 15025521291\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-790528a-5841893\right){x}-2033260063a-15025521291$ |
| 4.1-b3 |
4.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$1.99413$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.543135817$ |
$13.68783852$ |
3.769065024 |
\( \frac{34191163052375}{262144} a - \frac{286859170558125}{262144} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 6743607 a + 49834362\) , \( 40609623584 a + 300099713904\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(6743607a+49834362\right){x}+40609623584a+300099713904$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.20687$ |
$(59a-495), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.582609582$ |
$5.028263423$ |
5.940813929 |
\( -\frac{2402023}{768} a - \frac{2967337}{128} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -404883088 a - 2992032116\) , \( -12673316733993 a - 93654124086941\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-404883088a-2992032116\right){x}-12673316733993a-93654124086941$ |
| 6.1-b1 |
6.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.20687$ |
$(59a-495), (454a-3809)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041973565$ |
$34.24868686$ |
1.457605814 |
\( -\frac{2402023}{768} a - \frac{2967337}{128} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 2511 a - 21048\) , \( -985156 a + 8265344\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2511a-21048\right){x}-985156a+8265344$ |
| 6.2-a1 |
6.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.20687$ |
$(-59a-436), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.582609582$ |
$5.028263423$ |
5.940813929 |
\( \frac{2402023}{768} a - \frac{20206045}{768} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 404883088 a - 3396915204\) , \( 12673316733993 a - 106327440820934\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(404883088a-3396915204\right){x}+12673316733993a-106327440820934$ |
| 6.2-b1 |
6.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$2.20687$ |
$(-59a-436), (454a-3809)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041973565$ |
$34.24868686$ |
1.457605814 |
\( \frac{2402023}{768} a - \frac{20206045}{768} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -2511 a - 18537\) , \( 985156 a + 7280188\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2511a-18537\right){x}+985156a+7280188$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$32.67282208$ |
4.141111937 |
\( \frac{2185}{4} a - \frac{5963}{2} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 615 a + 4554\) , \( 11408 a + 84309\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(615a+4554\right){x}+11408a+84309$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{24} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.396274103$ |
$13.75407087$ |
4.144847179 |
\( -\frac{61511525}{65536} a - \frac{222233313}{32768} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -306291799791 a - 2263455638698\) , \( 274031630762693489 a + 2025057282941004146\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-306291799791a-2263455638698\right){x}+274031630762693489a+2025057282941004146$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{24} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$3.083744743$ |
3.126790121 |
\( -\frac{61511525}{65536} a - \frac{222233313}{32768} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -64 a + 530\) , \( 1632 a - 13681\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-64a+530\right){x}+1632a-13681$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.222936144$ |
$10.66129029$ |
1.807473038 |
\( \frac{2185}{4} a - \frac{5963}{2} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 758794082 a - 6366181194\) , \( 35677694904796 a - 299331112228424\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(758794082a-6366181194\right){x}+35677694904796a-299331112228424$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{6} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$32.67282208$ |
4.141111937 |
\( -\frac{2185}{4} a - \frac{9741}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -583 a + 5200\) , \( -6854 a + 58548\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-583a+5200\right){x}-6854a+58548$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{24} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.396274103$ |
$13.75407087$ |
4.144847179 |
\( \frac{61511525}{65536} a - \frac{505978151}{65536} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 306291799791 a - 2569747438489\) , \( -274031630762693489 a + 2299088913703697635\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(306291799791a-2569747438489\right){x}-274031630762693489a+2299088913703697635$ |
| 8.2-c1 |
8.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{24} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$3.083744743$ |
3.126790121 |
\( \frac{61511525}{65536} a - \frac{505978151}{65536} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 62 a + 466\) , \( -1633 a - 12049\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(62a+466\right){x}-1633a-12049$ |
| 8.2-d1 |
8.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{6} \) |
$2.37143$ |
$(-59a-436), (59a-495)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.222936144$ |
$10.66129029$ |
1.807473038 |
\( -\frac{2185}{4} a - \frac{9741}{4} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -758794052 a - 5607387081\) , \( -35684061085960 a - 263700462555782\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-758794052a-5607387081\right){x}-35684061085960a-263700462555782$ |
| 10.2-a1 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.936872239$ |
$21.59673281$ |
3.534500871 |
\( \frac{743967}{8000} a + \frac{3854291}{4000} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -2117010 a + 17761496\) , \( -10803776493 a + 90642247179\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2117010a+17761496\right){x}-10803776493a+90642247179$ |
| 10.2-a2 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{18} \cdot 5 \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.645624079$ |
$21.59673281$ |
3.534500871 |
\( \frac{8025743347527}{1310720} a + \frac{29314806044891}{655360} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 102990805 a - 864079084\) , \( -1600261541361 a + 13425981367840\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(102990805a-864079084\right){x}-1600261541361a+13425981367840$ |
| 10.2-a3 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{9} \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$5.810616717$ |
$2.399636979$ |
3.534500871 |
\( \frac{122931271240967}{7812500} a + \frac{454221647547291}{3906250} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 19566030 a - 164156324\) , \( 338336181254 a - 2838595534434\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(19566030a-164156324\right){x}+338336181254a-2838595534434$ |
| 10.2-b1 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.705946639$ |
$15.86116074$ |
0.946119306 |
\( \frac{743967}{8000} a + \frac{3854291}{4000} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -377849 a - 2792188\) , \( 31582418 a + 233389960\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-377849a-2792188\right){x}+31582418a+233389960$ |
| 10.2-b2 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{18} \cdot 5 \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.117839919$ |
$1.762351193$ |
0.946119306 |
\( \frac{8025743347527}{1310720} a + \frac{29314806044891}{655360} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -19947514 a - 147409408\) , \( -136332744923 a - 1007480841593\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-19947514a-147409408\right){x}-136332744923a-1007480841593$ |
| 10.2-b3 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{9} \) |
$2.50748$ |
$(59a-495), (18a-151)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.235315546$ |
$15.86116074$ |
0.946119306 |
\( \frac{122931271240967}{7812500} a + \frac{454221647547291}{3906250} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -22060889 a - 163026968\) , \( 158298257589 a + 1169803057191\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-22060889a-163026968\right){x}+158298257589a+1169803057191$ |
| 10.3-a1 |
10.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{18} \cdot 5 \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.645624079$ |
$21.59673281$ |
3.534500871 |
\( -\frac{8025743347527}{1310720} a + \frac{66655355437309}{1310720} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -102990807 a - 761088278\) , \( 1600261541360 a + 11825719826480\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-102990807a-761088278\right){x}+1600261541360a+11825719826480$ |
| 10.3-a2 |
10.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{9} \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$5.810616717$ |
$2.399636979$ |
3.534500871 |
\( -\frac{122931271240967}{7812500} a + \frac{1031374566335549}{7812500} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -19566032 a - 144590293\) , \( -338336181255 a - 2500259353179\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-19566032a-144590293\right){x}-338336181255a-2500259353179$ |
| 10.3-a3 |
10.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.936872239$ |
$21.59673281$ |
3.534500871 |
\( -\frac{743967}{8000} a + \frac{8452549}{8000} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 2117008 a + 15644487\) , \( 10803776492 a + 79838470687\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(2117008a+15644487\right){x}+10803776492a+79838470687$ |
| 10.3-b1 |
10.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{18} \cdot 5 \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.117839919$ |
$1.762351193$ |
0.946119306 |
\( -\frac{8025743347527}{1310720} a + \frac{66655355437309}{1310720} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 19947513 a - 167356922\) , \( 136332744923 a - 1143813586516\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(19947513a-167356922\right){x}+136332744923a-1143813586516$ |
| 10.3-b2 |
10.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{9} \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.235315546$ |
$15.86116074$ |
0.946119306 |
\( -\frac{122931271240967}{7812500} a + \frac{1031374566335549}{7812500} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 22060888 a - 185087857\) , \( -158298257589 a + 1328101314780\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(22060888a-185087857\right){x}-158298257589a+1328101314780$ |
| 10.3-b3 |
10.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{3} \) |
$2.50748$ |
$(-59a-436), (-18a-133)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.705946639$ |
$15.86116074$ |
0.946119306 |
\( -\frac{743967}{8000} a + \frac{8452549}{8000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 377848 a - 3170037\) , \( -31582418 a + 264972378\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(377848a-3170037\right){x}-31582418a+264972378$ |
| 12.1-a1 |
12.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 23 \) |
$1$ |
$3.693492967$ |
5.383508944 |
\( -\frac{162079163}{25165824} a + \frac{64054337}{12582912} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -273712644 a - 2022700010\) , \( -41718432950544 a - 308293667574996\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-273712644a-2022700010\right){x}-41718432950544a-308293667574996$ |
| 12.1-b1 |
12.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 23 \) |
$1$ |
$3.693492967$ |
5.383508944 |
\( \frac{162079163}{25165824} a - \frac{33970489}{25165824} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 273712643 a - 2296412653\) , \( 41718432950543 a - 350012100525539\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(273712643a-2296412653\right){x}+41718432950543a-350012100525539$ |
| 12.1-c1 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{25} \cdot 3^{3} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$4.708715726$ |
4.476041016 |
\( -\frac{6735610805}{9437184} a + \frac{60348342679}{9437184} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 9095547498 a + 67214885578\) , \( -2390819420870331 a - 17667837347663533\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9095547498a+67214885578\right){x}-2390819420870331a-17667837347663533$ |
| 12.1-c2 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{20} \cdot 3^{6} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$9.417431452$ |
4.476041016 |
\( \frac{156590819}{27648} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 12174123 a - 102139276\) , \( -54138691126 a + 454216413700\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(12174123a-102139276\right){x}-54138691126a+454216413700$ |
| 12.1-c3 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{25} \cdot 3^{3} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$9.417431452$ |
4.476041016 |
\( \frac{6735610805}{9437184} a + \frac{26806365937}{4718592} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9119 a - 67374\) , \( 1256853 a + 9287987\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9119a-67374\right){x}+1256853a+9287987$ |
| 12.1-c4 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{12} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$4.708715726$ |
4.476041016 |
\( \frac{555209567459}{23328} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 185638443 a - 1557481836\) , \( -3867072587286 a + 32444224373540\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(185638443a-1557481836\right){x}-3867072587286a+32444224373540$ |
| 12.1-d1 |
12.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{25} \cdot 3^{3} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$9.417431452$ |
4.476041016 |
\( -\frac{6735610805}{9437184} a + \frac{60348342679}{9437184} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 9121 a - 76493\) , \( -1247733 a + 10468347\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9121a-76493\right){x}-1247733a+10468347$ |
| 12.1-d2 |
12.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{20} \cdot 3^{6} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$9.417431452$ |
4.476041016 |
\( \frac{156590819}{27648} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -12174124 a - 89965153\) , \( 54138691125 a + 400077722574\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12174124a-89965153\right){x}+54138691125a+400077722574$ |
| 12.1-d3 |
12.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{25} \cdot 3^{3} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$4.708715726$ |
4.476041016 |
\( \frac{6735610805}{9437184} a + \frac{26806365937}{4718592} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -9095547496 a + 76310433075\) , \( 2390828516417828 a - 20058733078966939\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9095547496a+76310433075\right){x}+2390828516417828a-20058733078966939$ |
| 12.1-d4 |
12.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{12} \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$4.708715726$ |
4.476041016 |
\( \frac{555209567459}{23328} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -185638444 a - 1371843393\) , \( 3867072587285 a + 28577151786254\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-185638444a-1371843393\right){x}+3867072587285a+28577151786254$ |
| 12.1-e1 |
12.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.03853418$ |
0.699538680 |
\( \frac{162079163}{25165824} a - \frac{33970489}{25165824} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 9436 a + 69734\) , \( 7904308 a + 58411774\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(9436a+69734\right){x}+7904308a+58411774$ |
| 12.1-f1 |
12.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (59a-495), (454a-3809)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.03853418$ |
0.699538680 |
\( -\frac{162079163}{25165824} a + \frac{64054337}{12582912} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -9437 a + 79171\) , \( -7904309 a + 66316083\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-9437a+79171\right){x}-7904309a+66316083$ |
| 12.2-a1 |
12.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$2.62442$ |
$(59a-495), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1.613439338$ |
$25.25023603$ |
5.163550229 |
\( -\frac{1381}{3} a - \frac{10201}{3} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -2340 a - 17177\) , \( 180797 a + 1336304\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2340a-17177\right){x}+180797a+1336304$ |
| 12.2-b1 |
12.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$2.62442$ |
$(59a-495), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.422777721$ |
$14.74068177$ |
2.369633830 |
\( -\frac{1381}{3} a - \frac{10201}{3} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -17461706 a + 146501417\) , \( -3825208288641 a + 32092988479362\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-17461706a+146501417\right){x}-3825208288641a+32092988479362$ |
| 12.3-a1 |
12.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1.613439338$ |
$25.25023603$ |
5.163550229 |
\( \frac{1381}{3} a - \frac{11582}{3} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2340 a - 19517\) , \( -180797 a + 1517101\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(2340a-19517\right){x}-180797a+1517101$ |
| 12.3-b1 |
12.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$2.62442$ |
$(-59a-436), (454a-3809)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.422777721$ |
$14.74068177$ |
2.369633830 |
\( \frac{1381}{3} a - \frac{11582}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 17461704 a + 129039713\) , \( 3825208288640 a + 28267780190722\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(17461704a+129039713\right){x}+3825208288640a+28267780190722$ |
| 15.1-a1 |
15.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{3} \) |
$2.77499$ |
$(454a-3809), (-18a-133)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$20.44760815$ |
3.887443546 |
\( \frac{16980143}{375} a + \frac{125469254}{375} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 6225468 a - 52230749\) , \( 178041834494 a - 1493747297223\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(6225468a-52230749\right){x}+178041834494a-1493747297223$ |
| 15.1-b1 |
15.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{249}) \) |
$2$ |
$[2, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5 \) |
$2.77499$ |
$(454a-3809), (-18a-133)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$30.72106798$ |
3.893737156 |
\( -\frac{21007}{5} a + \frac{456767}{15} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 22208198654 a - 186323831161\) , \( 4988735946424272 a - 41854830684679477\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(22208198654a-186323831161\right){x}+4988735946424272a-41854830684679477$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
