| 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 |
| 24843.6-a1 |
24843.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{2} \cdot 13^{18} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.197394986$ |
0.911728387 |
\( -\frac{7241190483343322}{489259787572101} a + \frac{7346309553009001}{489259787572101} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 286 a - 218\) , \( 3616 a + 15106\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(286a-218\right){x}+3616a+15106$ |
| 24843.6-a2 |
24843.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{5} \cdot 13^{9} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.789579945$ |
0.911728387 |
\( -\frac{9158885728}{15824991} a + \frac{56008788119}{15824991} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84 a + 92\) , \( -44 a - 180\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-84a+92\right){x}-44a-180$ |
| 24843.6-a3 |
24843.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{12} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.394789972$ |
0.911728387 |
\( \frac{254107553040}{33787663} a + \frac{14410599351623}{709540923} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -484 a + 587\) , \( 1180 a + 4102\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-484a+587\right){x}+1180a+4102$ |
| 24843.6-a4 |
24843.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{5} \cdot 13^{9} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.197394986$ |
0.911728387 |
\( \frac{1850779593982650}{5274997} a + \frac{15470303228300719}{47474973} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -7654 a + 9312\) , \( 85080 a + 257246\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-7654a+9312\right){x}+85080a+257246$ |
| 24843.6-b1 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4803 a + 1055\) , \( 36894 a - 168194\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4803a+1055\right){x}+36894a-168194$ |
| 24843.6-b2 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{16} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 238 a - 510\) , \( 7812 a - 11501\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-510\right){x}+7812a-11501$ |
| 24843.6-b3 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.912776968$ |
2.208684594 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -7 a + 15\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+15\right){x}$ |
| 24843.6-b4 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.956388484$ |
2.208684594 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 28 a - 60\) , \( 36 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a-60\right){x}+36a-53$ |
| 24843.6-b5 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6007 a + 1525\) , \( 167514 a - 132740\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6007a+1525\right){x}+167514a-132740$ |
| 24843.6-b6 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 273 a - 585\) , \( -3240 a + 4770\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(273a-585\right){x}-3240a+4770$ |
| 24843.6-b7 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{8} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 343 a - 735\) , \( 4896 a - 7208\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(343a-735\right){x}+4896a-7208$ |
| 24843.6-b8 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 5488 a - 11760\) , \( 306540 a - 451295\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5488a-11760\right){x}+306540a-451295$ |
| 24843.6-c1 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{9} \cdot 13^{8} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.194404083$ |
3.591655993 |
\( \frac{76454964731374322}{974251369} a - \frac{201501804445240541}{2922754107} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2082 a + 7957\) , \( -248464 a + 37285\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-2082a+7957\right){x}-248464a+37285$ |
| 24843.6-c2 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{3} \cdot 13^{7} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.555232665$ |
3.591655993 |
\( \frac{16760032}{1911} a - \frac{23122025}{1911} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 13 a - 33\) , \( -43 a + 76\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(13a-33\right){x}-43a+76$ |
| 24843.6-c3 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{3} \cdot 13^{14} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.194404083$ |
3.591655993 |
\( \frac{4356902909358218}{1079211743883} a - \frac{8864911898113289}{3237635231649} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 968 a + 697\) , \( 11478 a - 26833\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(968a+697\right){x}+11478a-26833$ |
| 24843.6-c4 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{6} \cdot 13^{8} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.777616332$ |
3.591655993 |
\( \frac{85625872}{405769} a - \frac{1018148029}{1217307} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -62 a + 7\) , \( -350 a + 251\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-62a+7\right){x}-350a+251$ |
| 24843.6-c5 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{6} \cdot 13^{10} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.388808166$ |
3.591655993 |
\( -\frac{1707495993704}{205724883} a + \frac{102569051509}{617174649} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -117 a + 487\) , \( -3901 a + 376\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-117a+487\right){x}-3901a+376$ |
| 24843.6-c6 |
24843.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{9} \cdot 13^{7} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.388808166$ |
3.591655993 |
\( -\frac{140052466565944}{224827239} a + \frac{466181945434565}{224827239} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1207 a + 167\) , \( -16607 a + 11186\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-1207a+167\right){x}-16607a+11186$ |
*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.
