| 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 |
| 24843.4-a1 |
24843.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{2} \cdot 13^{18} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.197394986$ |
0.911728387 |
\( \frac{7241190483343322}{489259787572101} a + \frac{105119069665679}{489259787572101} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -286 a + 68\) , \( -3616 a + 18722\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-286a+68\right){x}-3616a+18722$ |
| 24843.4-a2 |
24843.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{5} \cdot 13^{9} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.789579945$ |
0.911728387 |
\( \frac{9158885728}{15824991} a + \frac{46849902391}{15824991} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 84 a + 8\) , \( 44 a - 224\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(84a+8\right){x}+44a-224$ |
| 24843.4-a3 |
24843.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{12} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.394789972$ |
0.911728387 |
\( -\frac{254107553040}{33787663} a + \frac{19746857965463}{709540923} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 484 a + 103\) , \( -1180 a + 5282\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(484a+103\right){x}-1180a+5282$ |
| 24843.4-a4 |
24843.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{5} \cdot 13^{9} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.197394986$ |
0.911728387 |
\( -\frac{1850779593982650}{5274997} a + \frac{32127319574144569}{47474973} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 7654 a + 1658\) , \( -85080 a + 342326\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(7654a+1658\right){x}-85080a+342326$ |
| 24843.4-b1 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1525 a + 6007\) , \( -167514 a + 34774\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1525a+6007\right){x}-167514a+34774$ |
| 24843.4-b2 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{16} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 510 a - 238\) , \( -7812 a - 3689\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(510a-238\right){x}-7812a-3689$ |
| 24843.4-b3 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.912776968$ |
2.208684594 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -15 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-15a+7\right){x}$ |
| 24843.4-b4 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.956388484$ |
2.208684594 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 60 a - 28\) , \( -36 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(60a-28\right){x}-36a-17$ |
| 24843.4-b5 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1055 a - 4803\) , \( -36894 a - 131300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1055a-4803\right){x}-36894a-131300$ |
| 24843.4-b6 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 7^{2} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 585 a - 273\) , \( 3240 a + 1530\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(585a-273\right){x}+3240a+1530$ |
| 24843.4-b7 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{8} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.478194242$ |
2.208684594 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 735 a - 343\) , \( -4896 a - 2312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(735a-343\right){x}-4896a-2312$ |
| 24843.4-b8 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.239097121$ |
2.208684594 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 11760 a - 5488\) , \( -306540 a - 144755\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(11760a-5488\right){x}-306540a-144755$ |
| 24843.4-c1 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 7^{6} \cdot 13^{10} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.388808166$ |
3.591655993 |
\( \frac{1707495993704}{205724883} a - \frac{5019918929603}{617174649} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 369 a - 486\) , \( 3900 a - 3525\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(369a-486\right){x}+3900a-3525$ |
| 24843.4-c2 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{3} \cdot 13^{7} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.555232665$ |
3.591655993 |
\( -\frac{16760032}{1911} a - \frac{6361993}{1911} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -21 a + 34\) , \( 42 a + 33\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-21a+34\right){x}+42a+33$ |
| 24843.4-c3 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{6} \cdot 13^{8} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.777616332$ |
3.591655993 |
\( -\frac{85625872}{405769} a - \frac{761270413}{1217307} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -56 a - 6\) , \( 349 a - 99\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-56a-6\right){x}+349a-99$ |
| 24843.4-c4 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 7^{3} \cdot 13^{14} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.194404083$ |
3.591655993 |
\( -\frac{4356902909358218}{1079211743883} a + \frac{4205796829961365}{3237635231649} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 1664 a - 696\) , \( -11479 a - 15355\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(1664a-696\right){x}-11479a-15355$ |
| 24843.4-c5 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{9} \cdot 13^{7} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.388808166$ |
3.591655993 |
\( \frac{140052466565944}{224827239} a + \frac{326129478868621}{224827239} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -1041 a - 166\) , \( 16606 a - 5421\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1041a-166\right){x}+16606a-5421$ |
| 24843.4-c6 |
24843.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 7^{9} \cdot 13^{8} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.194404083$ |
3.591655993 |
\( -\frac{76454964731374322}{974251369} a + \frac{27863089748882425}{2922754107} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5874 a - 7956\) , \( 248463 a - 211179\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(5874a-7956\right){x}+248463a-211179$ |
*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.
