| 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 |
| 13475.1-a1 |
13475.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{2} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$2.156720598$ |
5.202205821 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 a - 4\) , \( a - 3\bigr] \) |
${y}^2+{y}={x}^{3}+\left(6a-4\right){x}+a-3$ |
| 13475.1-b1 |
13475.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{2} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.806767612$ |
1.945996699 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -267 a + 178\) , \( 1181 a - 3248\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-267a+178\right){x}+1181a-3248$ |
| 13475.1-b2 |
13475.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{12} \cdot 11^{6} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.268922537$ |
1.945996699 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -147 a + 98\) , \( 2401 a - 6603\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-147a+98\right){x}+2401a-6603$ |
| 13475.1-b3 |
13475.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{18} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.089640845$ |
1.945996699 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 1323 a - 882\) , \( -63259 a + 173962\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1323a-882\right){x}-63259a+173962$ |
| 13475.1-c1 |
13475.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{6} \cdot 11^{4} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.745862362$ |
$1.062332908$ |
7.361723511 |
\( \frac{4657463}{41503} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 9 a - 6\) , \( 33 a - 112\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-6\right){x}+33a-112$ |
| 13475.1-c2 |
13475.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{12} \cdot 11^{2} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.872931181$ |
$0.531166454$ |
7.361723511 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -156 a + 104\) , \( 594 a - 1311\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-156a+104\right){x}+594a-1311$ |
*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.
