| 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 |
| 16.1-b1 |
16.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.18548$ |
$(a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$11.53162527$ |
1.738457921 |
\( -32768 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a$ |
| 16.1-b2 |
16.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.18548$ |
$(a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$11.53162527$ |
1.738457921 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a$ |
| 25.2-a1 |
25.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 6 a - 14\) , \( -9 a + 27\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-14\right){x}-9a+27$ |
| 25.2-a2 |
25.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 6 a - 14\) , \( 9 a - 30\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-14\right){x}+9a-30$ |
| 25.3-a1 |
25.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -6 a - 14\) , \( 9 a + 27\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-14\right){x}+9a+27$ |
| 25.3-a2 |
25.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.32541$ |
$(-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.31419920$ |
1.554924035 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -6 a - 14\) , \( -9 a - 30\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-14\right){x}-9a-30$ |
| 121.1-c1 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.96590$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.3 |
$1$ |
\( 2 \) |
$0.089785156$ |
$23.06325055$ |
1.248701727 |
\( -32768 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7\) , \( 10\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7{x}+10$ |
| 121.1-c2 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$1.96590$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.8 |
$1$ |
\( 2 \) |
$0.987636717$ |
$2.096659141$ |
1.248701727 |
\( -32768 \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7\) , \( -13\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-7{x}-13$ |
| 256.1-e1 |
256.1-e |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.37096$ |
$(a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.260975223$ |
$11.53162527$ |
3.629555552 |
\( -32768 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 160 a - 527\) , \( 2235 a - 7414\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(160a-527\right){x}+2235a-7414$ |
| 256.1-e2 |
256.1-e |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$2.37096$ |
$(a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.260975223$ |
$11.53162527$ |
3.629555552 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 160 a - 527\) , \( -2235 a + 7414\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(160a-527\right){x}-2235a+7414$ |
| 361.2-b1 |
361.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$2.58370$ |
$(2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.226142726$ |
$1.595318399$ |
2.141578668 |
\( -32768 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -106 a - 350\) , \( -968 a - 3213\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-106a-350\right){x}-968a-3213$ |
| 361.2-b2 |
361.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$2.58370$ |
$(2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.202376611$ |
$17.54850239$ |
2.141578668 |
\( -32768 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -106 a - 350\) , \( 968 a + 3210\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-106a-350\right){x}+968a+3210$ |
| 361.3-b1 |
361.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
361.3 |
\( 19^{2} \) |
\( 19^{6} \) |
$2.58370$ |
$(-2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.226142726$ |
$1.595318399$ |
2.141578668 |
\( -32768 \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 106 a - 350\) , \( 968 a - 3213\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(106a-350\right){x}+968a-3213$ |
| 361.3-b2 |
361.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
361.3 |
\( 19^{2} \) |
\( 19^{6} \) |
$2.58370$ |
$(-2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.202376611$ |
$17.54850239$ |
2.141578668 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 106 a - 350\) , \( -968 a + 3210\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(106a-350\right){x}-968a+3210$ |
*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.
