| 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 |
| 4096.1-CMb1 |
4096.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.260975223$ |
$5.765812638$ |
3.629555552 |
\( -32768 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+1$ |
| 4096.1-CMa1 |
4096.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.260975223$ |
$5.765812638$ |
3.629555552 |
\( -32768 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-1$ |
| 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-b1 |
4096.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
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 |
\( -1024 a + 2560 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}+1$ |
| 4096.1-c1 |
4096.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{28} \) |
$2.37096$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 1 \) |
$1$ |
$2.741783643$ |
1.653357745 |
\( 1024 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 6\) , \( 4 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-6\right){x}+4a+1$ |
| 4096.1-d1 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$2.126572485$ |
$6.875185818$ |
4.408271033 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 4096.1-d2 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{24} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.253144970$ |
$3.437592909$ |
4.408271033 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4{x}$ |
| 4096.1-d3 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{30} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.126572485$ |
$1.718796454$ |
4.408271033 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( -112\bigr] \) |
${y}^2={x}^{3}-44{x}-112$ |
| 4096.1-d4 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{30} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$8.506289940$ |
$1.718796454$ |
4.408271033 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( 112\bigr] \) |
${y}^2={x}^{3}-44{x}+112$ |
| 4096.1-e1 |
4096.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{28} \) |
$2.37096$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 1 \) |
$1$ |
$2.741783643$ |
1.653357745 |
\( 1024 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 6\) , \( -4 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-6\right){x}-4a-1$ |
| 4096.1-f1 |
4096.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
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 |
\( -1024 a + 2560 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a\) , \( -1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-1$ |
| 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 |
\( 1024 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( a - 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(a-1\right){x}-1$ |
*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.
