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 |
121.2-a3 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.83826$ |
$(a+3), (a-3)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$0.915095465$ |
$9.257718117$ |
0.479231487 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
1936.2-c3 |
1936.2-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1936.2 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$1.67652$ |
$(a), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.507203009$ |
$4.628859058$ |
3.320249936 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+1$ |
9801.8-e3 |
9801.8-e |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9801.8 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{2} \) |
$2.51479$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1.724111421$ |
$3.085906039$ |
7.524246676 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) |
${y}^2+{y}={x}^{3}-3{x}-5$ |
11979.10-c3 |
11979.10-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.10 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(a-1), (a+3), (a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.611561869$ |
4.558185304 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 6 a - 6\) , \( 19 a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a-6\right){x}+19a-3$ |
11979.11-a3 |
11979.11-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.11 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.529443744$ |
$1.611561869$ |
2.413302695 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 2 a + 10\) , \( 23 a - 22\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+10\right){x}+23a-22$ |
11979.2-a3 |
11979.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.2 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(-a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.529443744$ |
$1.611561869$ |
2.413302695 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2 a + 10\) , \( -23 a - 22\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+10\right){x}-23a-22$ |
11979.3-c3 |
11979.3-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.3 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(-a-1), (a+3), (a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.611561869$ |
4.558185304 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 6\) , \( -20 a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-6\right){x}-20a-3$ |
14641.3-d3 |
14641.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14641.3 |
\( 11^{4} \) |
\( 11^{14} \) |
$2.78020$ |
$(a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1.070445924$ |
$0.841610737$ |
5.096253114 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-40{x}-221$ |
34969.4-c3 |
34969.4-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34969.4 |
\( 11^{2} \cdot 17^{2} \) |
\( 11^{2} \cdot 17^{6} \) |
$3.45624$ |
$(a+3), (a-3), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$2.245326449$ |
3.175371117 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 4 a - 1\) , \( -7 a - 5\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a-1\right){x}-7a-5$ |
34969.6-c3 |
34969.6-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34969.6 |
\( 11^{2} \cdot 17^{2} \) |
\( 11^{2} \cdot 17^{6} \) |
$3.45624$ |
$(a+3), (a-3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$2.245326449$ |
3.175371117 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -4 a - 1\) , \( 6 a - 5\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4a-1\right){x}+6a-5$ |
*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.