| 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 |
| 675.6-a1 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.023955633$ |
1.234936958 |
\( -\frac{349209575}{59049} a - \frac{298597801}{19683} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -32 a - 39\) , \( 181 a + 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32a-39\right){x}+181a+11$ |
| 675.6-a2 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.023955633$ |
1.234936958 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -39 a - 23\) , \( -138 a + 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a-23\right){x}-138a+63$ |
| 675.6-a3 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.047911266$ |
1.234936958 |
\( -\frac{77935}{243} a - \frac{11594}{81} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3 a - 9\) , \( 10 a - 7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-9\right){x}+10a-7$ |
| 675.6-a4 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{12} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.047911266$ |
1.234936958 |
\( \frac{77935}{243} a - \frac{112717}{243} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -4 a + 7\) , \( -4 a - 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+7\right){x}-4a-15$ |
| 675.6-a5 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( -\frac{2927543402641}{3486784401} a + \frac{1635099303025}{3486784401} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -9 a - 158\) , \( -174 a + 1125\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-158\right){x}-174a+1125$ |
| 675.6-a6 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{27} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( \frac{2927543402641}{3486784401} a - \frac{430814699872}{1162261467} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -97 a + 66\) , \( -64 a + 926\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-97a+66\right){x}-64a+926$ |
| 675.6-a7 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( -\frac{54238838797}{243} a + \frac{90191354077}{243} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -629 a - 368\) , \( -9778 a + 3693\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-629a-368\right){x}-9778a+3693$ |
| 675.6-a8 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -527 a - 624\) , \( 9910 a + 1568\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-527a-624\right){x}+9910a+1568$ |
*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.
