| 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 |
| 224.2-a1 |
224.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.2 |
\( 2^{5} \cdot 7 \) |
\( 2^{13} \cdot 7 \) |
$0.91464$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.956842684$ |
1.479234028 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -22 a + 87\) , \( -162 a - 91\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-22a+87\right){x}-162a-91$ |
| 784.2-a1 |
784.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
784.2 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{7} \) |
$1.25103$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.739617014$ |
1.118195819 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 149 a - 597\) , \( 1964 a - 5468\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(149a-597\right){x}+1964a-5468$ |
| 896.2-a1 |
896.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.2 |
\( 2^{7} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.691498443$ |
$1.383696732$ |
1.446582121 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 107 a - 128\) , \( -577 a + 141\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(107a-128\right){x}-577a+141$ |
| 896.5-a1 |
896.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.5 |
\( 2^{7} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 213 a + 42\) , \( 80 a + 2300\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(213a+42\right){x}+80a+2300$ |
| 3584.7-a1 |
3584.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.7 |
\( 2^{9} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.691848366$ |
1.045976412 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -468 a + 384\) , \( -2140 a + 7060\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-468a+384\right){x}-2140a+7060$ |
| 6272.2-d1 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.517549865$ |
$0.522988206$ |
4.799608661 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -746 a + 896\) , \( 424 a - 14864\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-746a+896\right){x}+424a-14864$ |
| 7168.5-b1 |
7168.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -171 a - 511\) , \( 2369 a + 3929\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-171a-511\right){x}+2369a+3929$ |
| 7168.7-f1 |
7168.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.691848366$ |
2.091952824 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -468 a + 384\) , \( 2140 a - 7060\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-468a+384\right){x}+2140a-7060$ |
| 12544.5-i1 |
12544.5-i |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{7} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.687071516$ |
$0.369808507$ |
3.772952634 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1493 a - 297\) , \( -31268 a + 18636\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-1493a-297\right){x}-31268a+18636$ |
| 13552.4-a1 |
13552.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.4 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{13} \cdot 7 \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.617918128$ |
$0.590010268$ |
2.886403740 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -534 a - 254\) , \( 7479 a - 1907\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-534a-254\right){x}+7479a-1907$ |
| 13552.6-c1 |
13552.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.6 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{13} \cdot 7 \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.590010268$ |
3.568046726 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 661 a - 256\) , \( -4844 a - 5221\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(661a-256\right){x}-4844a-5221$ |
| 18144.2-a1 |
18144.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.2 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{13} \cdot 3^{12} \cdot 7 \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.765787282$ |
$0.652280894$ |
3.020742951 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -191 a + 769\) , \( 4751 a + 933\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-191a+769\right){x}+4751a+933$ |
| 25088.7-d1 |
25088.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{31} \cdot 7^{7} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.276096762$ |
$0.261494103$ |
4.171724484 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3283 a - 2690\) , \( 77889 a + 9318\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3283a-2690\right){x}+77889a+9318$ |
| 28672.7-k1 |
28672.7-k |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.489210671$ |
1.479234028 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 853 a + 169\) , \( -809 a - 16525\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(853a+169\right){x}-809a-16525$ |
| 28672.7-t1 |
28672.7-t |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.550706080$ |
$0.489210671$ |
5.252325258 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 853 a + 169\) , \( 809 a + 16525\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(853a+169\right){x}+809a+16525$ |
*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.
