| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$1.00252$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$15.70093405$ |
1.664295681 |
\( -\frac{143041}{2} a - \frac{606189}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1515 a - 7916\) , \( -99637 a + 519800\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1515a-7916\right){x}-99637a+519800$ |
| 2.1-a2 |
2.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$1.00252$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$15.70093405$ |
1.664295681 |
\( \frac{4559}{32} a + \frac{14691}{32} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 8 a + 27\) , \( 16 a + 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+27\right){x}+16a+63$ |
| 2.2-a1 |
2.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$1.00252$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$15.70093405$ |
1.664295681 |
\( \frac{143041}{2} a - 374615 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -1517 a - 6400\) , \( 99636 a + 420163\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-1517a-6400\right){x}+99636a+420163$ |
| 2.2-a2 |
2.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( 2^{5} \) |
$1.00252$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$15.70093405$ |
1.664295681 |
\( -\frac{4559}{32} a + \frac{9625}{16} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 4 a + 11\) , \( 6 a + 23\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(4a+11\right){x}+6a+23$ |
| 4.1-a1 |
4.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.28205935$ |
1.049730474 |
\( -\frac{818172355}{1024} a - \frac{3448457287}{1024} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -716 a + 3738\) , \( -1996 a + 10404\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-716a+3738\right){x}-1996a+10404$ |
| 4.1-a2 |
4.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{36} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.475784373$ |
1.049730474 |
\( -\frac{1224782159965}{1073741824} a - \frac{2581999137701}{536870912} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -9585 a - 40413\) , \( -1212620 a - 5113612\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-9585a-40413\right){x}-1212620a-5113612$ |
| 4.1-a3 |
4.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{36} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.475784373$ |
1.049730474 |
\( \frac{1224782159965}{1073741824} a - \frac{6388780435367}{1073741824} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 9584 a - 49997\) , \( 1212619 a - 6326231\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9584a-49997\right){x}+1212619a-6326231$ |
| 4.1-a4 |
4.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.28205935$ |
1.049730474 |
\( \frac{818172355}{1024} a - \frac{2133314821}{512} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 715 a + 3022\) , \( 1995 a + 8408\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(715a+3022\right){x}+1995a+8408$ |
| 4.1-b1 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.09362683$ |
0.534961152 |
\( -\frac{12925019097}{32} a + \frac{67429479645}{32} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 5 a - 28\) , \( 13 a - 66\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(5a-28\right){x}+13a-66$ |
| 4.1-b2 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.09362683$ |
0.534961152 |
\( -\frac{940219731}{1048576} a + \frac{2452520565}{524288} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 72875 a - 380188\) , \( -20764677 a + 108329124\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(72875a-380188\right){x}-20764677a+108329124$ |
| 4.1-b3 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.18725366$ |
0.534961152 |
\( -\frac{11856277583953155}{32} a + \frac{30927044151883341}{16} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4715 a - 19883\) , \( 177745 a + 749549\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-4715a-19883\right){x}+177745a+749549$ |
| 4.1-b4 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.09362683$ |
0.534961152 |
\( \frac{940219731}{1048576} a + \frac{3964821399}{1048576} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -72875 a - 307313\) , \( 20764677 a + 87564447\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-72875a-307313\right){x}+20764677a+87564447$ |
| 4.1-b5 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.18725366$ |
0.534961152 |
\( -\frac{6410589075}{1024} a + \frac{16753979061}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2365 a - 9973\) , \( -133485 a - 562905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-2365a-9973\right){x}-133485a-562905$ |
| 4.1-b6 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.18725366$ |
0.534961152 |
\( \frac{6410589075}{1024} a + \frac{27097369047}{1024} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 2365 a - 12338\) , \( 133485 a - 696390\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(2365a-12338\right){x}+133485a-696390$ |
| 4.1-b7 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.09362683$ |
0.534961152 |
\( \frac{12925019097}{32} a + \frac{13626115137}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -5 a - 23\) , \( -13 a - 53\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5a-23\right){x}-13a-53$ |
| 4.1-b8 |
4.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$1.19220$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.18725366$ |
0.534961152 |
\( \frac{11856277583953155}{32} a + \frac{49997810719813527}{32} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 4715 a - 24598\) , \( -177745 a + 927294\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(4715a-24598\right){x}-177745a+927294$ |
| 4.2-a1 |
4.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.19220$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.036370603$ |
$47.26998531$ |
1.093433119 |
\( -2051 a - 19799 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -14 a - 53\) , \( 34 a + 148\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a-53\right){x}+34a+148$ |
| 4.3-a1 |
4.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.19220$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.036370603$ |
$47.26998531$ |
1.093433119 |
\( 2051 a - 21850 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 12 a - 65\) , \( -35 a + 183\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(12a-65\right){x}-35a+183$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$1.41777$ |
$(a+4), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.155996037$ |
$8.682861923$ |
1.722910452 |
\( -\frac{3645}{16} a + \frac{4347}{8} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -8316 a + 43371\) , \( 324545 a - 1693155\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8316a+43371\right){x}+324545a-1693155$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{12} \) |
$1.41777$ |
$(a+4), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.155996037$ |
$8.682861923$ |
1.722910452 |
\( \frac{3645}{16} a + \frac{5049}{16} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 8317 a + 35077\) , \( -316229 a - 1333533\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(8317a+35077\right){x}-316229a-1333533$ |
| 10.1-a1 |
10.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{6} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.10412336$ |
0.747517043 |
\( \frac{10248729}{31250} a + \frac{48360866}{15625} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a + 11\) , \( 2 a - 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+11\right){x}+2a-8$ |
| 10.1-a2 |
10.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{3} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.10412336$ |
0.747517043 |
\( \frac{852883061}{500} a + \frac{1798735919}{250} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -265 a - 1114\) , \( -4596 a - 19380\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-265a-1114\right){x}-4596a-19380$ |
| 10.1-b1 |
10.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{3} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.810242456$ |
$16.76637336$ |
1.079991629 |
\( -\frac{4602102825621}{2000} a + \frac{12004564630091}{1000} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 45081 a - 235181\) , \( -11390518 a + 59424228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(45081a-235181\right){x}-11390518a+59424228$ |
| 10.1-b2 |
10.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.405121228$ |
$16.76637336$ |
1.079991629 |
\( -\frac{61683314403}{4000000} a + \frac{166104912613}{2000000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 7 a - 26\) , \( -12 a + 56\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-26\right){x}-12a+56$ |
| 10.1-b3 |
10.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.202560614$ |
$16.76637336$ |
1.079991629 |
\( \frac{33372655241}{8192000} a + \frac{77750803889}{4096000} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -289 a - 1211\) , \( 5248 a + 22126\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-289a-1211\right){x}+5248a+22126$ |
| 10.1-b4 |
10.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{12} \) |
$1.49911$ |
$(a-5), (4a-21)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.202560614$ |
$4.191593340$ |
1.079991629 |
\( \frac{1250388843910793}{3906250000} a + \frac{2636397421418697}{1953125000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 2 a - 11\) , \( -38 a + 198\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-11\right){x}-38a+198$ |
| 10.2-a1 |
10.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{4} \) |
$1.49911$ |
$(a-5), (4a+17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041880808$ |
$26.39678212$ |
0.937477868 |
\( -\frac{12145582503}{80000} a - \frac{25625382399}{40000} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 19676 a - 102652\) , \( -7387714 a + 38541634\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(19676a-102652\right){x}-7387714a+38541634$ |
| 10.3-a1 |
10.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.3 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{4} \) |
$1.49911$ |
$(a+4), (4a-21)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.041880808$ |
$26.39678212$ |
0.937477868 |
\( \frac{12145582503}{80000} a - \frac{63396347301}{80000} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -19676 a - 82976\) , \( 7368038 a + 31070944\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-19676a-82976\right){x}+7368038a+31070944$ |
| 10.4-a1 |
10.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{6} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.10412336$ |
0.747517043 |
\( -\frac{10248729}{31250} a + \frac{106970461}{31250} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a + 10\) , \( -2 a - 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a+10\right){x}-2a-6$ |
| 10.4-a2 |
10.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{3} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.10412336$ |
0.747517043 |
\( -\frac{852883061}{500} a + \frac{4450354899}{500} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 267 a - 1379\) , \( 4862 a - 25355\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(267a-1379\right){x}+4862a-25355$ |
| 10.4-b1 |
10.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{12} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.202560614$ |
$4.191593340$ |
1.079991629 |
\( -\frac{1250388843910793}{3906250000} a + \frac{6523183686748187}{3906250000} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -9\) , \( 37 a + 151\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-9{x}+37a+151$ |
| 10.4-b2 |
10.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.202560614$ |
$16.76637336$ |
1.079991629 |
\( -\frac{33372655241}{8192000} a + \frac{188874263019}{8192000} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 289 a - 1500\) , \( -5248 a + 27374\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(289a-1500\right){x}-5248a+27374$ |
| 10.4-b3 |
10.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.405121228$ |
$16.76637336$ |
1.079991629 |
\( \frac{61683314403}{4000000} a + \frac{270526510823}{4000000} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -5 a - 19\) , \( 6 a + 25\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-19\right){x}+6a+25$ |
| 10.4-b4 |
10.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{3} \) |
$1.49911$ |
$(a+4), (4a+17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.810242456$ |
$16.76637336$ |
1.079991629 |
\( \frac{4602102825621}{2000} a + \frac{19407026434561}{2000} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -45081 a - 190100\) , \( 11390518 a + 48033710\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-45081a-190100\right){x}+11390518a+48033710$ |
| 16.2-a1 |
16.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{13} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.85120170$ |
3.474334122 |
\( -\frac{850323}{8} a + \frac{4449865}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 6 a + 15\) , \( 9 a + 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+15\right){x}+9a+49$ |
| 16.2-a2 |
16.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{17} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.85120170$ |
3.474334122 |
\( \frac{14739}{64} a + \frac{34391}{64} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 270 a - 1402\) , \( -11156 a + 58204\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(270a-1402\right){x}-11156a+58204$ |
| 16.2-b1 |
16.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{11} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.867330994$ |
3.095616321 |
\( \frac{1311463}{8} a - \frac{6833509}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 35147 a + 148230\) , \( -6225753 a - 26253930\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(35147a+148230\right){x}-6225753a-26253930$ |
| 16.2-c1 |
16.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.68602$ |
$(a+4), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.455459150$ |
$4.834673697$ |
1.867289193 |
\( -\frac{16835}{64} a - \frac{73799}{64} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a + 5\) , \( -5 a - 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(a+5\right){x}-5a-21$ |
| 16.3-a1 |
16.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{17} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.85120170$ |
3.474334122 |
\( -\frac{14739}{64} a + \frac{24565}{32} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -270 a - 1132\) , \( 11156 a + 47048\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-270a-1132\right){x}+11156a+47048$ |
| 16.3-a2 |
16.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{13} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$21.85120170$ |
3.474334122 |
\( \frac{850323}{8} a + \frac{1799771}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 5 a + 23\) , \( 6 a + 26\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+23\right){x}+6a+26$ |
| 16.3-b1 |
16.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{11} \) |
$1.68602$ |
$(a+4), (a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.867330994$ |
3.095616321 |
\( -\frac{1311463}{8} a - \frac{2761023}{4} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -35147 a + 183377\) , \( 6225753 a - 32479683\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-35147a+183377\right){x}+6225753a-32479683$ |
| 16.3-c1 |
16.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.68602$ |
$(a+4), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.455459150$ |
$4.834673697$ |
1.867289193 |
\( \frac{16835}{64} a - \frac{45317}{32} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -a + 6\) , \( 5 a - 26\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-a+6\right){x}+5a-26$ |
| 16.4-a1 |
16.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.68602$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.941716602$ |
$14.34901929$ |
2.864688726 |
\( 2051 a - 21850 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1842 a - 7770\) , \( 96300 a + 406095\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-1842a-7770\right){x}+96300a+406095$ |
| 16.4-b1 |
16.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{13} \) |
$1.68602$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.552268367$ |
$3.214116582$ |
1.505243559 |
\( -\frac{143041}{2} a - \frac{606189}{2} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -29330 a - 123684\) , \( -5955681 a - 25115055\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-29330a-123684\right){x}-5955681a-25115055$ |
| 16.4-b2 |
16.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{17} \) |
$1.68602$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.110453673$ |
$16.07058291$ |
1.505243559 |
\( \frac{4559}{32} a + \frac{14691}{32} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 20 a - 104\) , \( -391 a + 2033\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(20a-104\right){x}-391a+2033$ |
| 16.5-a1 |
16.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.68602$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.941716602$ |
$14.34901929$ |
2.864688726 |
\( -2051 a - 19799 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1840 a - 9612\) , \( -96301 a + 502395\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1840a-9612\right){x}-96301a+502395$ |
| 16.5-b1 |
16.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{13} \) |
$1.68602$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.552268367$ |
$3.214116582$ |
1.505243559 |
\( \frac{143041}{2} a - 374615 \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 29330 a - 153014\) , \( 5955680 a - 31070736\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(29330a-153014\right){x}+5955680a-31070736$ |
| 16.5-b2 |
16.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{17} \) |
$1.68602$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.110453673$ |
$16.07058291$ |
1.505243559 |
\( -\frac{4559}{32} a + \frac{9625}{16} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -20 a - 84\) , \( 390 a + 1642\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-20a-84\right){x}+390a+1642$ |
| 18.1-a1 |
18.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{3} \cdot 3^{8} \) |
$1.73641$ |
$(a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.48012418$ |
0.979444622 |
\( -\frac{39001}{216} a + \frac{702745}{648} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 254 a - 1320\) , \( 1589 a - 8304\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(254a-1320\right){x}+1589a-8304$ |
| 18.1-a2 |
18.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{89}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.73641$ |
$(a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.48012418$ |
0.979444622 |
\( \frac{8153785}{12288} a + \frac{34224773}{12288} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -42 a - 171\) , \( -194 a - 821\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-42a-171\right){x}-194a-821$ |
*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.
