| 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 |
| 1024.1-a1 |
1024.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.67652$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$0.181270444$ |
$3.350074985$ |
1.464789341 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 1\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-1\right){x}-2a+1$ |
| 1024.1-e1 |
1024.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.67652$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.350074985$ |
4.040342453 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 1\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-1\right){x}+2a-1$ |
| 4096.1-a1 |
4096.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$0.149304605$ |
$6.700149971$ |
2.412966943 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a-1\right){x}+1$ |
| 4096.1-g1 |
4096.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$6.700149971$ |
4.040342453 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( a - 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(a-1\right){x}-1$ |
| 9216.1-b1 |
9216.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$1.934166694$ |
2.332692803 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 9\) , \( 14 a - 7\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-9\right){x}+14a-7$ |
| 9216.1-d1 |
9216.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1.398495310$ |
$1.934166694$ |
6.524519890 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 9\) , \( -14 a + 7\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a-9\right){x}-14a+7$ |
| 9216.3-a1 |
9216.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$0.361577141$ |
$1.934166694$ |
1.686896791 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 8\) , \( 16\bigr] \) |
${y}^2={x}^{3}+\left(-8a+8\right){x}+16$ |
| 9216.3-e1 |
9216.3-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$1.934166694$ |
2.332692803 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 8\) , \( -16\bigr] \) |
${y}^2={x}^{3}+\left(-8a+8\right){x}-16$ |
| 25600.1-a1 |
25600.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$1.498199079$ |
1.806896075 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 25\) , \( -6 a + 31\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-25\right){x}-6a+31$ |
| 25600.1-i1 |
25600.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$2.174039774$ |
$1.498199079$ |
7.856527872 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 25\) , \( 6 a - 31\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-25\right){x}+6a-31$ |
| 25600.3-a1 |
25600.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$0.506763109$ |
$1.498199079$ |
1.831336549 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 23\) , \( -14 a + 7\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+23\right){x}-14a+7$ |
| 25600.3-i1 |
25600.3-i |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$1.498199079$ |
1.806896075 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a + 23\) , \( 14 a - 7\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a+23\right){x}+14a-7$ |
| 36864.1-b1 |
36864.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$0.655366408$ |
$3.868333389$ |
3.057537011 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 3\) , \( -1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-3\right){x}-1$ |
| 36864.1-i1 |
36864.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$0.643837466$ |
$3.868333389$ |
3.003750049 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a - 3\) , \( 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-a-3\right){x}+1$ |
| 36864.3-a1 |
36864.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$1.135323379$ |
$3.868333389$ |
5.296721352 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+\left(-2a+2\right){x}-2$ |
| 36864.3-k1 |
36864.3-k |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2Cn, 3Nn |
$1$ |
\( 1 \) |
$2.864824586$ |
$3.868333389$ |
13.36551138 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+\left(-2a+2\right){x}+2$ |
*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.
