| 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-a6 |
224.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.5 |
\( 2^{5} \cdot 7 \) |
\( 2^{10} \cdot 7^{4} \) |
$0.91464$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.913685369$ |
1.479234028 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 1\) , \( -3 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-3a+1$ |
| 784.4-a6 |
784.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
784.4 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.25103$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.479234028$ |
1.118195819 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 16 a - 4\) , \( 8 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(16a-4\right){x}+8a+24$ |
| 896.4-a6 |
896.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.4 |
\( 2^{7} \cdot 7 \) |
\( 2^{22} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.956842684$ |
1.479234028 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 14\) , \( 12 a - 24\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-14\right){x}+12a-24$ |
| 896.7-a6 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{16} \cdot 7^{4} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.172874610$ |
$2.767393464$ |
1.446582121 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3 a - 5\) , \( -6 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a-5\right){x}-6a-2$ |
| 3584.4-a6 |
3584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15 a + 25\) , \( -3 a - 47\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-15a+25\right){x}-3a-47$ |
| 6272.7-d6 |
6272.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.7 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.517549865$ |
$1.045976412$ |
4.799608661 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -31 a + 36\) , \( -37 a + 126\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-31a+36\right){x}-37a+126$ |
| 7168.5-f6 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -15 a + 25\) , \( 3 a + 47\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-15a+25\right){x}+3a+47$ |
| 7168.7-b6 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{28} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12 a + 16\) , \( 48 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(12a+16\right){x}+48a-48$ |
| 12544.5-g6 |
12544.5-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{10} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.687071516$ |
$0.739617014$ |
3.772952634 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a + 95\) , \( -260 a - 72\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-9a+95\right){x}-260a-72$ |
| 13552.10-c6 |
13552.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.10 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{4} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.180020537$ |
3.568046726 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 12 a - 39\) , \( -81 a + 67\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-39\right){x}-81a+67$ |
| 13552.12-a6 |
13552.12-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.12 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{4} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.404479532$ |
$1.180020537$ |
2.886403740 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 36\) , \( 72 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+36{x}+72a-20$ |
| 18144.5-a6 |
18144.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.5 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{4} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.765787282$ |
$1.304561789$ |
3.020742951 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -21 a + 3\) , \( 39 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-21a+3\right){x}+39a-17$ |
| 25088.4-e6 |
25088.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.319024190$ |
$0.522988206$ |
4.171724484 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 106 a - 173\) , \( 747 a - 203\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a-173\right){x}+747a-203$ |
| 28672.7-h6 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a - 55\) , \( -41 a + 147\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-55\right){x}-41a+147$ |
| 28672.7-w6 |
28672.7-w |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{34} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.887676520$ |
$0.978421342$ |
5.252325258 |
\( -\frac{361845}{196} a + \frac{274391}{196} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 55\) , \( 41 a - 147\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-55\right){x}+41a-147$ |
*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.
