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 |
64.1-a1 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.746658170$ |
0.561425840 |
\( -72061125694419920 a^{2} + 39990907711475312 a + 161919879656286672 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1742 a^{2} - 971 a - 3929\) , \( 42399 a^{2} - 23535 a - 95292\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1742a^{2}-971a-3929\right){x}+42399a^{2}-23535a-95292$ |
64.1-a2 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.746658170$ |
0.561425840 |
\( 32070217982944608 a^{2} - 72061125694419920 a + 25718317995977536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 72 a^{2} + 4 a - 264\) , \( 500 a^{2} - 16 a - 1624\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(72a^{2}+4a-264\right){x}+500a^{2}-16a-1624$ |
64.1-a3 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.986632680$ |
0.561425840 |
\( 406749952 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 102 a^{2} - 61 a - 244\) , \( 640 a^{2} - 360 a - 1460\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(102a^{2}-61a-244\right){x}+640a^{2}-360a-1460$ |
64.1-a4 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.746658170$ |
0.561425840 |
\( 39990907711475312 a^{2} + 32070217982944608 a - 22193279444028480 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 131 a - 199\) , \( -6 a^{2} - 855 a - 1073\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-131a-199\right){x}-6a^{2}-855a-1073$ |
64.1-a5 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$47.15977059$ |
0.561425840 |
\( -208912 a^{2} + 65520 a + 561936 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a^{2} - 11 a - 49\) , \( 55 a^{2} - 31 a - 124\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(22a^{2}-11a-49\right){x}+55a^{2}-31a-124$ |
64.1-a6 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$47.15977059$ |
0.561425840 |
\( 65520 a^{2} + 143392 a + 78592 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 11 a - 39\) , \( -46 a^{2} + 25 a + 103\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-11a-39\right){x}-46a^{2}+25a+103$ |
64.1-a7 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$188.6390823$ |
0.561425840 |
\( 1792 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a^{2} - a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a^{2}-a-4\right){x}$ |
64.1-a8 |
64.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{24} \) |
$1.25103$ |
$(2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$47.15977059$ |
0.561425840 |
\( 143392 a^{2} - 208912 a + 66240 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a^{2} + 4 a + 16\) , \( 4 a^{2} - 8\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-8a^{2}+4a+16\right){x}+4a^{2}-8$ |
*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.