| 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 |
| 1296.3-a1 |
1296.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.163308669$ |
$5.108115717$ |
2.359472722 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 1296.3-a2 |
1296.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.489926008$ |
$1.702705239$ |
2.359472722 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \) |
${y}^2={x}^{3}+27$ |
| 1296.3-a3 |
1296.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.326617338$ |
$5.108115717$ |
2.359472722 |
\( 54000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2{x}+5$ |
| 1296.3-a4 |
1296.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.979852016$ |
$1.702705239$ |
2.359472722 |
\( 54000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -32\) , \( -57\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-32{x}-57$ |
| 1296.3-b1 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.605891169$ |
1.713719018 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 36\) , \( 572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+36{x}+572$ |
| 1296.3-b2 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.423564678$ |
1.713719018 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \) |
${y}^2={x}^{3}+6{x}+7$ |
| 1296.3-b3 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.423564678$ |
1.713719018 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -9\) , \( -4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-9{x}-4$ |
| 1296.3-b4 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{20} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.211782339$ |
1.713719018 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -54\) , \( 176\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-54{x}+176$ |
| 1296.3-b5 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{32} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.302945584$ |
1.713719018 |
\( -\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 630 a + 756\) , \( -3276 a + 14324\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(630a+756\right){x}-3276a+14324$ |
| 1296.3-b6 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{32} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.302945584$ |
1.713719018 |
\( \frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -630 a + 756\) , \( 3276 a + 14324\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-630a+756\right){x}+3276a+14324$ |
| 1296.3-b7 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.211782339$ |
1.713719018 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -144\) , \( -598\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-144{x}-598$ |
| 1296.3-b8 |
1296.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1296.3 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.51647$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.605891169$ |
1.713719018 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -864\) , \( 10220\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-864{x}+10220$ |
*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.
