| 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-a2 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{10} \) |
$0.83826$ |
$(a+3), (a-3)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5^{2} \) |
$0.183019093$ |
$1.851543623$ |
0.479231487 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 1936.2-c2 |
1936.2-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1936.2 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 11^{10} \) |
$1.67652$ |
$(a), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$2.536015047$ |
$0.925771811$ |
3.320249936 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -199\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-199$ |
| 9801.8-e2 |
9801.8-e |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9801.8 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{10} \) |
$2.51479$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$8.620557108$ |
$0.617181207$ |
7.524246676 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -93\) , \( 625\bigr] \) |
${y}^2+{y}={x}^{3}-93{x}+625$ |
| 11979.10-c2 |
11979.10-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.10 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{16} \) |
$2.64417$ |
$(a-1), (a+3), (a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.322312373$ |
4.558185304 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 206 a - 176\) , \( -3231 a + 37\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(206a-176\right){x}-3231a+37$ |
| 11979.11-a2 |
11979.11-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.11 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{16} \) |
$2.64417$ |
$(a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.647218722$ |
$0.322312373$ |
2.413302695 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 82 a + 320\) , \( -2607 a + 2038\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(82a+320\right){x}-2607a+2038$ |
| 11979.2-a2 |
11979.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.2 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{16} \) |
$2.64417$ |
$(-a-1), (a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.647218722$ |
$0.322312373$ |
2.413302695 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -82 a + 320\) , \( 2607 a + 2038\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-82a+320\right){x}+2607a+2038$ |
| 11979.3-c2 |
11979.3-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11979.3 |
\( 3^{2} \cdot 11^{3} \) |
\( 3^{6} \cdot 11^{16} \) |
$2.64417$ |
$(-a-1), (a+3), (a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.322312373$ |
4.558185304 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -206 a - 176\) , \( 3230 a + 37\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-206a-176\right){x}+3230a+37$ |
| 14641.3-d2 |
14641.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14641.3 |
\( 11^{4} \) |
\( 11^{22} \) |
$2.78020$ |
$(a+3), (a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$5.352229620$ |
$0.168322147$ |
5.096253114 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-1250{x}+31239$ |
| 34969.4-c2 |
34969.4-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34969.4 |
\( 11^{2} \cdot 17^{2} \) |
\( 11^{10} \cdot 17^{6} \) |
$3.45624$ |
$(a+3), (a-3), (-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.449065289$ |
3.175371117 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 124 a - 11\) , \( 883 a + 1125\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(124a-11\right){x}+883a+1125$ |
| 34969.6-c2 |
34969.6-c |
$3$ |
$25$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34969.6 |
\( 11^{2} \cdot 17^{2} \) |
\( 11^{10} \cdot 17^{6} \) |
$3.45624$ |
$(a+3), (a-3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.449065289$ |
3.175371117 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -124 a - 11\) , \( -884 a + 1125\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-124a-11\right){x}-884a+1125$ |
*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.
