| 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 |
| 675.5-b5 |
675.5-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.5 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{13} \cdot 5^{13} \) |
$1.51064$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$0.661104577$ |
1.594644241 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 77 a + 63\) , \( -104 a + 706\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(77a+63\right){x}-104a+706$ |
| 675.8-b5 |
675.8-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.8 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{13} \cdot 5^{13} \) |
$1.51064$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.661104577$ |
1.594644241 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 86 a - 120\) , \( 447 a - 108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(86a-120\right){x}+447a-108$ |
| 3375.10-b5 |
3375.10-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.10 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.034839496$ |
$0.295654955$ |
4.427953515 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -278 a - 540\) , \( -3566 a - 4170\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-278a-540\right){x}-3566a-4170$ |
| 3375.11-b5 |
3375.11-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.11 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.513465836$ |
$0.295654955$ |
3.584939154 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 190 a + 663\) , \( -4485 a + 6129\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(190a+663\right){x}-4485a+6129$ |
| 3375.6-b5 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.209455486$ |
$0.295654955$ |
3.584939154 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 268 a - 822\) , \( 3819 a - 7339\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(268a-822\right){x}+3819a-7339$ |
| 3375.7-b5 |
3375.7-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.7 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{13} \cdot 5^{19} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$0.776129622$ |
$0.295654955$ |
4.427953515 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -348 a + 757\) , \( -1336 a - 6945\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-348a+757\right){x}-1336a-6945$ |
| 16875.13-f6 |
16875.13-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{13} \cdot 5^{25} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.132220915$ |
1.275715392 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2174 a - 3041\) , \( 57214 a - 23151\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2174a-3041\right){x}+57214a-23151$ |
| 16875.8-f6 |
16875.8-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{13} \cdot 5^{25} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.132220915$ |
1.275715392 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 1930 a + 1594\) , \( -18108 a + 101405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1930a+1594\right){x}-18108a+101405$ |
| 27225.5-b6 |
27225.5-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{7} \cdot 5^{13} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$3.048265448$ |
$0.345250605$ |
5.077043362 |
\( -\frac{93926997067673}{19775390625} a + \frac{66606305361919}{6591796875} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 361 a - 125\) , \( -2070 a - 3220\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(361a-125\right){x}-2070a-3220$ |
*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.
