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 |
75.1-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.322695746 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
75.1-a8 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.322695746 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
147.2-a1 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{20} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.431038464$ |
0.497720347 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-470a+321\right){x}+1866a-3772$ |
147.2-a2 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{20} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.431038464$ |
0.497720347 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 470 a - 149\) , \( -1866 a - 1906\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(470a-149\right){x}-1866a-1906$ |
192.1-a3 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.908836754$ |
0.524717144 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(16a-16\right){x}-180$ |
192.1-a8 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.908836754$ |
0.524717144 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -384 a + 384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-384a+384\right){x}-2772$ |
228.1-a1 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{2} \cdot 19^{10} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.548223191$ |
0.633033614 |
\( -\frac{612993539767699445}{588582360748896} a + \frac{16582918214994847}{73572795093612} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 142 a - 105\) , \( 756 a + 161\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(142a-105\right){x}+756a+161$ |
228.1-a3 |
228.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3 \cdot 19^{5} \) |
$0.60143$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.096446383$ |
0.633033614 |
\( \frac{38854777864121}{7606576128} a - \frac{17432772730153}{7606576128} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -18 a + 55\) , \( 148 a + 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a+55\right){x}+148a+1$ |
228.2-a1 |
228.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.2 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{2} \cdot 19^{10} \) |
$0.60143$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.548223191$ |
0.633033614 |
\( \frac{612993539767699445}{588582360748896} a - \frac{160110064682580223}{196194120249632} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -140 a + 35\) , \( -615 a + 881\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-140a+35\right){x}-615a+881$ |
228.2-a3 |
228.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
228.2 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3 \cdot 19^{5} \) |
$0.60143$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.096446383$ |
0.633033614 |
\( -\frac{38854777864121}{7606576128} a + \frac{1338875320873}{475411008} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -167 a + 113\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a+35\right){x}-167a+113$ |
241.1-a1 |
241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.1 |
\( 241 \) |
\( 241 \) |
$0.60982$ |
$(-16a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2.204799027$ |
0.636470655 |
\( -\frac{1030333071375}{241} a + \frac{124584645375}{241} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -80 a + 85\) , \( -33 a - 241\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-80a+85\right){x}-33a-241$ |
241.2-a1 |
241.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.2 |
\( 241 \) |
\( 241 \) |
$0.60982$ |
$(16a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2.204799027$ |
0.636470655 |
\( \frac{1030333071375}{241} a - \frac{905748426000}{241} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 79 a + 5\) , \( 32 a - 274\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(79a+5\right){x}+32a-274$ |
273.1-a6 |
273.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.1 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{4} \cdot 7^{16} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (-3a+1), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.537289970$ |
0.620409017 |
\( -\frac{12221157721811331281}{3888252876643317} a + \frac{9513879748815593356}{1296084292214439} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -172 a + 250\) , \( -559 a - 702\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-172a+250\right){x}-559a-702$ |
273.1-a8 |
273.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.1 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{16} \cdot 7^{4} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (-3a+1), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.537289970$ |
0.620409017 |
\( \frac{16502205085237769}{204788493} a - \frac{54431432607484}{68262831} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -542 a + 1090\) , \( 8949 a + 3564\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-542a+1090\right){x}+8949a+3564$ |
273.4-a6 |
273.4-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.4 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{4} \cdot 7^{16} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.537289970$ |
0.620409017 |
\( \frac{12221157721811331281}{3888252876643317} a + \frac{16320481524635448787}{3888252876643317} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 170 a + 80\) , \( 558 a - 1260\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170a+80\right){x}+558a-1260$ |
273.4-a8 |
273.4-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.4 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3^{16} \cdot 7^{4} \cdot 13 \) |
$0.62913$ |
$(-2a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.537289970$ |
0.620409017 |
\( -\frac{16502205085237769}{204788493} a + \frac{16338910787415317}{204788493} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 540 a + 550\) , \( -8950 a + 12514\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(540a+550\right){x}-8950a+12514$ |
289.1-a4 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$0.63815$ |
$(17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2.123938699$ |
0.613128289 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$ |
343.2-a1 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{19} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( -\frac{2097781165791}{13841287201} a + \frac{1802695628925}{13841287201} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 6 a + 48\) , \( 416 a + 152\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a+48\right){x}+416a+152$ |
343.2-a2 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{19} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( \frac{2097781165791}{13841287201} a - \frac{295085536866}{13841287201} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -44 a + 56\) , \( -540 a + 143\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-44a+56\right){x}-540a+143$ |
343.2-a7 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{13} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( -\frac{308817493407}{2401} a + \frac{246921503922}{2401} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 786 a - 524\) , \( -6694 a - 433\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(786a-524\right){x}-6694a-433$ |
343.2-a8 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{13} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( \frac{308817493407}{2401} a - \frac{61895989485}{2401} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -464 a - 332\) , \( 6180 a + 1082\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-464a-332\right){x}+6180a+1082$ |
343.3-a1 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{19} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( -\frac{2097781165791}{13841287201} a + \frac{1802695628925}{13841287201} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -57 a + 46\) , \( 551 a - 453\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-57a+46\right){x}+551a-453$ |
343.3-a2 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{19} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( \frac{2097781165791}{13841287201} a - \frac{295085536866}{13841287201} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -49 a - 6\) , \( -417 a + 568\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-49a-6\right){x}-417a+568$ |
343.3-a7 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{13} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( -\frac{308817493407}{2401} a + \frac{246921503922}{2401} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 331 a + 464\) , \( -6181 a + 7262\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(331a+464\right){x}-6181a+7262$ |
343.3-a8 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{13} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$0.640604886$ |
0.739706807 |
\( \frac{308817493407}{2401} a - \frac{61895989485}{2401} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 523 a - 784\) , \( 6955 a - 6603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(523a-784\right){x}+6955a-6603$ |
363.1-a1 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{2} \) |
$0.67558$ |
$(-2a+1), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.025585977$ |
0.592122339 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$ |
399.2-a1 |
399.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.2 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{6} \cdot 7 \cdot 19^{8} \) |
$0.69174$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.621401725$ |
0.717532907 |
\( -\frac{1389689543960222201}{3209893414749} a - \frac{1078699815736689589}{3209893414749} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -153 a - 284\) , \( 1812 a + 1581\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-153a-284\right){x}+1812a+1581$ |
399.2-a2 |
399.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.2 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{24} \cdot 7 \cdot 19^{2} \) |
$0.69174$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.621401725$ |
0.717532907 |
\( \frac{111301988183011}{1342951407} a - \frac{118687708907161}{1342951407} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -283 a + 16\) , \( -1962 a + 1075\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-283a+16\right){x}-1962a+1075$ |
399.3-a1 |
399.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.3 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{6} \cdot 7 \cdot 19^{8} \) |
$0.69174$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.621401725$ |
0.717532907 |
\( \frac{1389689543960222201}{3209893414749} a - \frac{822796453232303930}{1069964471583} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 152 a - 436\) , \( -1813 a + 3394\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(152a-436\right){x}-1813a+3394$ |
399.3-a2 |
399.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.3 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{24} \cdot 7 \cdot 19^{2} \) |
$0.69174$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.621401725$ |
0.717532907 |
\( -\frac{111301988183011}{1342951407} a - \frac{2461906908050}{447650469} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 282 a - 266\) , \( 1961 a - 886\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(282a-266\right){x}+1961a-886$ |
475.1-a3 |
475.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.1 |
\( 5^{2} \cdot 19 \) |
\( 5^{2} \cdot 19^{8} \) |
$0.72256$ |
$(-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.449930551$ |
0.837117794 |
\( \frac{147104989379271}{84917815205} a - \frac{100481829971616}{84917815205} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -18 a + 22\) , \( 33 a + 28\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-18a+22\right){x}+33a+28$ |
475.2-a3 |
475.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.2 |
\( 5^{2} \cdot 19 \) |
\( 5^{2} \cdot 19^{8} \) |
$0.72256$ |
$(-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.449930551$ |
0.837117794 |
\( -\frac{147104989379271}{84917815205} a + \frac{9324631881531}{16983563041} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 17 a + 5\) , \( -34 a + 62\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a+5\right){x}-34a+62$ |
481.2-a1 |
481.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.2 |
\( 13 \cdot 37 \) |
\( 13 \cdot 37 \) |
$0.72483$ |
$(-4a+1), (-7a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.118200834$ |
$8.331786658$ |
0.568588478 |
\( -\frac{42208}{481} a - \frac{24959}{481} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
481.2-a2 |
481.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.2 |
\( 13 \cdot 37 \) |
\( 13^{2} \cdot 37^{2} \) |
$0.72483$ |
$(-4a+1), (-7a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059100417$ |
$4.165893329$ |
0.568588478 |
\( -\frac{7617412112}{231361} a + \frac{4002184503}{231361} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5\) , \( 3 a - 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+5{x}+3a-3$ |
481.3-a1 |
481.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.3 |
\( 13 \cdot 37 \) |
\( 13 \cdot 37 \) |
$0.72483$ |
$(4a-3), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.118200834$ |
$8.331786658$ |
0.568588478 |
\( \frac{42208}{481} a - \frac{67167}{481} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
481.3-a2 |
481.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.3 |
\( 13 \cdot 37 \) |
\( 13^{2} \cdot 37^{2} \) |
$0.72483$ |
$(4a-3), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059100417$ |
$4.165893329$ |
0.568588478 |
\( \frac{7617412112}{231361} a - \frac{3615227609}{231361} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( a + 5\) , \( -3 a + 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-3a+5$ |
507.2-a4 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{8} \cdot 13^{2} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.282583906$ |
$1.890295042$ |
0.616802873 |
\( \frac{37159393753}{1053} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -69\) , \( -252\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-69{x}-252$ |
579.1-a1 |
579.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3^{2} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075774335$ |
$7.505847337$ |
0.656736620 |
\( -\frac{12224}{579} a - \frac{9867}{193} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-{x}-a$ |
579.1-a2 |
579.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3 \cdot 193^{2} \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.151548671$ |
$3.752923668$ |
0.656736620 |
\( \frac{4604240642}{111747} a + \frac{23890776935}{111747} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 10 a - 6\) , \( -10 a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(10a-6\right){x}-10a$ |
579.1-b4 |
579.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3^{16} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.389035352$ |
0.801959934 |
\( \frac{545139180439}{1266273} a + \frac{76917924848}{1266273} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 37 a + 46\) , \( 186 a - 241\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(37a+46\right){x}+186a-241$ |
579.2-a1 |
579.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3^{2} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075774335$ |
$7.505847337$ |
0.656736620 |
\( \frac{12224}{579} a - \frac{41825}{579} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
579.2-a2 |
579.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3 \cdot 193^{2} \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.151548671$ |
$3.752923668$ |
0.656736620 |
\( -\frac{4604240642}{111747} a + \frac{28495017577}{111747} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -11 a + 5\) , \( 9 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+5\right){x}+9a-9$ |
579.2-b4 |
579.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3^{16} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.389035352$ |
0.801959934 |
\( -\frac{545139180439}{1266273} a + \frac{69117456143}{140697} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -38 a + 83\) , \( -187 a - 55\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+83\right){x}-187a-55$ |
588.2-a2 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.342545916$ |
0.791075908 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
588.2-a4 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.342545916$ |
0.791075908 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
603.1-a1 |
603.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.1 |
\( 3^{2} \cdot 67 \) |
\( 3^{26} \cdot 67 \) |
$0.76697$ |
$(-2a+1), (9a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.791616523$ |
0.914080025 |
\( \frac{64247275757}{3956283} a - \frac{6008441195}{439587} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 112 a + 16\) , \( -27 a + 525\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(112a+16\right){x}-27a+525$ |
603.1-a4 |
603.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.1 |
\( 3^{2} \cdot 67 \) |
\( 3^{11} \cdot 67^{4} \) |
$0.76697$ |
$(-2a+1), (9a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.791616523$ |
0.914080025 |
\( -\frac{107397602362141}{544080267} a + \frac{514170304798595}{544080267} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 142 a - 284\) , \( -1245 a + 1575\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(142a-284\right){x}-1245a+1575$ |
603.2-a1 |
603.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.2 |
\( 3^{2} \cdot 67 \) |
\( 3^{26} \cdot 67 \) |
$0.76697$ |
$(-2a+1), (9a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.791616523$ |
0.914080025 |
\( -\frac{64247275757}{3956283} a + \frac{10171305002}{3956283} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -113 a + 129\) , \( 26 a + 499\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-113a+129\right){x}+26a+499$ |
603.2-a4 |
603.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.2 |
\( 3^{2} \cdot 67 \) |
\( 3^{11} \cdot 67^{4} \) |
$0.76697$ |
$(-2a+1), (9a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.791616523$ |
0.914080025 |
\( \frac{107397602362141}{544080267} a + \frac{406772702436454}{544080267} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -143 a - 141\) , \( 1244 a + 331\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-143a-141\right){x}+1244a+331$ |
651.2-a2 |
651.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
651.2 |
\( 3 \cdot 7 \cdot 31 \) |
\( 3 \cdot 7^{8} \cdot 31^{2} \) |
$0.78180$ |
$(-2a+1), (-3a+1), (6a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.901914198$ |
1.041440810 |
\( \frac{356651947635794317}{16619921283} a - \frac{302247373300273970}{16619921283} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -314 a + 70\) , \( 2197 a - 1728\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-314a+70\right){x}+2197a-1728$ |
*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.