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 |
1568.2-a1 |
1568.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{3} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$0.168455059$ |
$3.319686739$ |
1.690916372 |
\( -\frac{16471}{4} a + \frac{2971}{4} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4 a + 5\) , \( a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-4a+5\right){x}+a+4$ |
1568.2-a2 |
1568.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{3} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{4} \) |
$0.084227529$ |
$3.319686739$ |
1.690916372 |
\( \frac{16471}{4} a - 3375 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -4 a\) , \( -4 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-4a{x}-4a+8$ |
1568.2-a3 |
1568.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{9} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \) |
$1.179185414$ |
$0.474240962$ |
1.690916372 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 116 a + 85\) , \( 191 a - 336\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(116a+85\right){x}+191a-336$ |
1568.2-a4 |
1568.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{9} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{4} \) |
$0.589592707$ |
$0.474240962$ |
1.690916372 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 86 a - 220\) , \( -44 a - 392\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(86a-220\right){x}-44a-392$ |
1568.2-b1 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{8} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.165438288$ |
2.251072633 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -3581 a + 2388\) , \( 55046 a - 134557\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3581a+2388\right){x}+55046a-134557$ |
1568.2-b2 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{27} \cdot 7^{9} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.496314864$ |
2.251072633 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 269 a + 194\) , \( 1017 a - 4482\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(269a+194\right){x}+1017a-4482$ |
1568.2-b3 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{27} \cdot 7^{9} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.496314864$ |
2.251072633 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 200 a - 507\) , \( 2267 a - 4120\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(200a-507\right){x}+2267a-4120$ |
1568.2-b4 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{17} \cdot 7^{7} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.488944592$ |
2.251072633 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 25 a - 17\) , \( -36 a - 46\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-17\right){x}-36a-46$ |
1568.2-b5 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{17} \cdot 7^{7} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.488944592$ |
2.251072633 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 24 a - 16\) , \( 44 a + 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(24a-16\right){x}+44a+12$ |
1568.2-b6 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{8} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.488944592$ |
2.251072633 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -11 a + 8\) , \( -16 a + 39\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-11a+8\right){x}-16a+39$ |
1568.2-b7 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{12} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.496314864$ |
2.251072633 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 94 a - 62\) , \( 362 a - 885\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(94a-62\right){x}+362a-885$ |
1568.2-b8 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{57} \cdot 7^{7} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.165438288$ |
2.251072633 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -606 a - 716\) , \( 5616 a - 23564\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-606a-716\right){x}+5616a-23564$ |
1568.2-b9 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{57} \cdot 7^{7} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.165438288$ |
2.251072633 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -395 a + 1383\) , \( 13026 a - 20402\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-395a+1383\right){x}+13026a-20402$ |
1568.2-b10 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{18} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.248157432$ |
2.251072633 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -746 a + 498\) , \( 4394 a - 10741\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-746a+498\right){x}+4394a-10741$ |
1568.2-b11 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{10} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.744472296$ |
2.251072633 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -221 a + 148\) , \( -772 a + 1887\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-221a+148\right){x}-772a+1887$ |
1568.2-b12 |
1568.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{10} \) |
$1.48773$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.082719144$ |
2.251072633 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -57341 a + 38228\) , \( 3474182 a - 8492445\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-57341a+38228\right){x}+3474182a-8492445$ |
*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.