| 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 |
| 224.5-a2 |
224.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.5 |
\( 2^{5} \cdot 7 \) |
\( 2^{5} \cdot 7^{2} \) |
$0.91464$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.913685369$ |
1.479234028 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a - 16\) , \( -12 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a-16\right){x}-12a+18$ |
| 784.4-a2 |
784.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
784.4 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{5} \cdot 7^{8} \) |
$1.25103$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.479234028$ |
1.118195819 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -14 a + 96\) , \( 287 a + 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a+96\right){x}+287a+36$ |
| 896.4-a2 |
896.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.4 |
\( 2^{7} \cdot 7 \) |
\( 2^{17} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.956842684$ |
1.479234028 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 40 a - 15\) , \( -74 a - 60\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(40a-15\right){x}-74a-60$ |
| 896.7-a2 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{11} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 8 a + 19\) , \( -33 a + 50\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(8a+19\right){x}-33a+50$ |
| 3584.4-a2 |
3584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -53 a - 51\) , \( -336 a - 23\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-53a-51\right){x}-336a-23$ |
| 6272.7-d2 |
6272.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.7 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.035099730$ |
$1.045976412$ |
4.799608661 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -68 a - 129\) , \( 470 a + 555\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-68a-129\right){x}+470a+555$ |
| 7168.5-f2 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -53 a - 51\) , \( 336 a + 23\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-53a-51\right){x}+336a+23$ |
| 7168.7-b2 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{23} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -65 a + 94\) , \( -23 a - 422\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-65a+94\right){x}-23a-422$ |
| 12544.5-g2 |
12544.5-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{17} \cdot 7^{8} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.374143032$ |
$0.739617014$ |
3.772952634 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -278 a + 100\) , \( -1637 a + 2594\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-278a+100\right){x}-1637a+2594$ |
| 13552.10-c2 |
13552.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.10 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{2} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.180020537$ |
3.568046726 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 96 a + 22\) , \( 35 a + 616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(96a+22\right){x}+35a+616$ |
| 13552.12-a2 |
13552.12-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.12 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{2} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.808959064$ |
$1.180020537$ |
2.886403740 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -110 a + 60\) , \( 351 a - 572\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-110a+60\right){x}+351a-572$ |
| 18144.5-a2 |
18144.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.5 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{5} \cdot 3^{12} \cdot 7^{2} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.531574565$ |
$1.304561789$ |
3.020742951 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 21 a - 126\) , \( 106 a - 574\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(21a-126\right){x}+106a-574$ |
| 25088.4-e2 |
25088.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638048381$ |
$0.522988206$ |
4.171724484 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 378 a + 355\) , \( 2695 a - 8107\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(378a+355\right){x}+2695a-8107$ |
| 28672.7-h2 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 159 a - 58\) , \( 491 a + 798\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(159a-58\right){x}+491a+798$ |
| 28672.7-w2 |
28672.7-w |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{29} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.775353040$ |
$0.978421342$ |
5.252325258 |
\( \frac{13647889}{14} a - \frac{94721547}{14} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 159 a - 58\) , \( -491 a - 798\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(159a-58\right){x}-491a-798$ |
*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.
