| 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-b3 |
675.5-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.5 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.51064$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$1.322209155$ |
1.594644241 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 2 a + 12\) , \( -34 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a+12\right){x}-34a+6$ |
| 675.8-b3 |
675.8-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.8 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.51064$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$1.322209155$ |
1.594644241 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 8 a - 5\) , \( a + 63\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(8a-5\right){x}+a+63$ |
| 3375.10-b3 |
3375.10-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.10 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1.552259244$ |
$0.591309910$ |
4.427953515 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -4 a - 64\) , \( 183 a - 629\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-64\right){x}+183a-629$ |
| 3375.11-b3 |
3375.11-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.11 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.418910972$ |
$0.591309910$ |
3.584939154 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -3 a + 65\) , \( -203 a - 353\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+65\right){x}-203a-353$ |
| 3375.6-b3 |
3375.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.6 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$1.256732918$ |
$0.591309910$ |
3.584939154 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 33 a - 47\) , \( 254 a + 339\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-47\right){x}+254a+339$ |
| 3375.7-b3 |
3375.7-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.7 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.517419748$ |
$0.591309910$ |
4.427953515 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -38 a + 37\) , \( 343 a - 437\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+37\right){x}+343a-437$ |
| 16875.13-f4 |
16875.13-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{20} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.264441831$ |
1.275715392 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 197 a - 101\) , \( 304 a + 6696\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(197a-101\right){x}+304a+6696$ |
| 16875.8-f4 |
16875.8-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{20} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.264441831$ |
1.275715392 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 77 a + 258\) , \( -4080 a + 947\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(77a+258\right){x}-4080a+947$ |
| 27225.5-b4 |
27225.5-b |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.762066362$ |
$0.690501211$ |
5.077043362 |
\( -\frac{1217478647}{11390625} a + \frac{227748383}{3796875} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 24 a + 13\) , \( 190 a - 370\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(24a+13\right){x}+190a-370$ |
*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.
