| 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-a3 |
224.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
224.5 |
\( 2^{5} \cdot 7 \) |
\( 2^{14} \cdot 7^{2} \) |
$0.91464$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.913685369$ |
1.479234028 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5\) , \( a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+5{x}+a-5$ |
| 784.4-a3 |
784.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
784.4 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{8} \) |
$1.25103$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.479234028$ |
1.118195819 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a - 28\) , \( -32 a - 60\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-28\right){x}-32a-60$ |
| 896.4-a3 |
896.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.4 |
\( 2^{7} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.956842684$ |
1.479234028 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 15\) , \( 44\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-13a+15\right){x}+44$ |
| 896.7-a3 |
896.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
896.7 |
\( 2^{7} \cdot 7 \) |
\( 2^{20} \cdot 7^{2} \) |
$1.29349$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.345749221$ |
$2.767393464$ |
1.446582121 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 3\) , \( 7 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-3\right){x}+7a+3$ |
| 3584.4-a3 |
3584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.383696732$ |
1.045976412 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 5\) , \( 15 a + 93\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-5\right){x}+15a+93$ |
| 6272.7-d3 |
6272.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.7 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.758774932$ |
$1.045976412$ |
4.799608661 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 46 a + 10\) , \( -4 a - 244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(46a+10\right){x}-4a-244$ |
| 7168.5-f3 |
7168.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a - 5\) , \( -15 a - 93\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(30a-5\right){x}-15a-93$ |
| 7168.7-b3 |
7168.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.7 |
\( 2^{10} \cdot 7 \) |
\( 2^{32} \cdot 7^{2} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.383696732$ |
2.091952824 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 42\) , \( -33 a + 90\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(11a-42\right){x}-33a+90$ |
| 12544.5-g3 |
12544.5-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.5 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{8} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.843535758$ |
$0.739617014$ |
3.772952634 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 93 a - 110\) , \( 524 a - 200\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(93a-110\right){x}+524a-200$ |
| 13552.10-c3 |
13552.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.10 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{2} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (-2a+3)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.180020537$ |
3.568046726 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -43 a + 25\) , \( 83 a - 153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-43a+25\right){x}+83a-153$ |
| 13552.12-a3 |
13552.12-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13552.12 |
\( 2^{4} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{2} \cdot 11^{6} \) |
$2.55087$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.808959064$ |
$1.180020537$ |
2.886403740 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 32 a - 48\) , \( -120 a + 100\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(32a-48\right){x}-120a+100$ |
| 18144.5-a3 |
18144.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18144.5 |
\( 2^{5} \cdot 3^{4} \cdot 7 \) |
\( 2^{14} \cdot 3^{12} \cdot 7^{2} \) |
$2.74392$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.382893641$ |
$1.304561789$ |
3.020742951 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 12 a + 36\) , \( -60 a + 104\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(12a+36\right){x}-60a+104$ |
| 25088.4-e3 |
25088.4-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{32} \cdot 7^{8} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.638048381$ |
$0.522988206$ |
4.171724484 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -203 a + 33\) , \( -1169 a + 1415\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-203a+33\right){x}-1169a+1415$ |
| 28672.7-h3 |
28672.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{38} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.978421342$ |
1.479234028 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -53 a + 62\) , \( 9 a - 246\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-53a+62\right){x}+9a-246$ |
| 28672.7-w3 |
28672.7-w |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{38} \cdot 7^{2} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.775353040$ |
$0.978421342$ |
5.252325258 |
\( \frac{1145925}{112} a - \frac{1290439}{112} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -53 a + 62\) , \( -9 a + 246\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-53a+62\right){x}-9a+246$ |
*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.
