| 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-a4 |
224.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.5 |
\( 2^{5} \cdot 7 \) |
\( 2^{19} \cdot 7 \) |
$0.91464$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.913685369$ |
1.479234028 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3\) , \( -a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-3{x}-a+1$ |
| 784.4-a4 |
784.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
784.4 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$1.25103$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.479234028$ |
1.118195819 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a + 12\) , \( 26 a - 40\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a+12\right){x}+26a-40$ |
| 896.4-a4 |
896.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.4 |
\( 2^{7} \cdot 7 \) |
\( 2^{31} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.956842684$ |
1.479234028 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 6\) , \( -16 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-6\right){x}-16a+4$ |
| 896.7-a4 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{25} \cdot 7 \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2 a + 1\) , \( 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2a+1\right){x}+5$ |
| 3584.4-a4 |
3584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -11 a + 1\) , \( -33 a + 39\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-11a+1\right){x}-33a+39$ |
| 6272.7-d4 |
6272.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.7 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.379387466$ |
$1.045976412$ |
4.799608661 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -19 a - 7\) , \( 85 a - 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-19a-7\right){x}+85a-27$ |
| 7168.5-f4 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 1\) , \( 33 a - 39\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-11a+1\right){x}+33a-39$ |
| 7168.7-b4 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{37} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 16\) , \( -36 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+16\right){x}-36a-20$ |
| 12544.5-g5 |
12544.5-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{31} \cdot 7^{7} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.421767879$ |
$0.739617014$ |
3.772952634 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -37 a + 39\) , \( -20 a + 380\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-37a+39\right){x}-20a+380$ |
| 13552.10-c5 |
13552.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.10 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{19} \cdot 7 \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.180020537$ |
3.568046726 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 16 a - 8\) , \( 48 a + 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(16a-8\right){x}+48a+32$ |
| 13552.12-a5 |
13552.12-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.12 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{19} \cdot 7 \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.617918128$ |
$1.180020537$ |
2.886403740 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -15 a + 18\) , \( -8 a - 74\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-15a+18\right){x}-8a-74$ |
| 18144.5-a5 |
18144.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.5 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{19} \cdot 3^{12} \cdot 7 \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.765787282$ |
$1.304561789$ |
3.020742951 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 15\) , \( -29 a - 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-3a-15\right){x}-29a-45$ |
| 25088.4-e5 |
25088.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{37} \cdot 7^{7} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.319024190$ |
$0.522988206$ |
4.171724484 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 78 a - 5\) , \( -243 a - 805\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(78a-5\right){x}-243a-805$ |
| 28672.7-h5 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{43} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 23\) , \( 105 a - 51\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-23\right){x}+105a-51$ |
| 28672.7-w5 |
28672.7-w |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{43} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.887676520$ |
$0.978421342$ |
5.252325258 |
\( \frac{138325}{1792} a - \frac{774199}{1792} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 23\) , \( -105 a + 51\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-23\right){x}-105a+51$ |
*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.
