| 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 |
| 2268.1-a4 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.432415362$ |
1.321137289 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 17\) , \( 6 a - 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-17\right){x}+6a-22$ |
| 15876.1-c1 |
15876.1-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.1 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{7} \) |
$1.73734$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.749014438$ |
1.729774751 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 194 a - 373\) , \( -1806 a + 2426\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(194a-373\right){x}-1806a+2426$ |
| 111132.3-a1 |
111132.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
111132.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{3} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{7} \) |
$2.82591$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$1$ |
$0.749014438$ |
0.864887375 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -278 a + 356\) , \( 716 a + 1746\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-278a+356\right){x}+716a+1746$ |
| 145152.1-b1 |
145152.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145152.1 |
\( 2^{8} \cdot 3^{4} \cdot 7 \) |
\( 2^{26} \cdot 3^{12} \cdot 7 \) |
$3.02103$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.495426483$ |
1.144138454 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 801 a - 657\) , \( -8652 a + 2382\bigr] \) |
${y}^2={x}^{3}+\left(801a-657\right){x}-8652a+2382$ |
| 145152.1-c1 |
145152.1-c |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145152.1 |
\( 2^{8} \cdot 3^{4} \cdot 7 \) |
\( 2^{26} \cdot 3^{6} \cdot 7 \) |
$3.02103$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.858103840$ |
1.981705933 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 219 a + 48\) , \( -432 a + 1658\bigr] \) |
${y}^2={x}^{3}+\left(219a+48\right){x}-432a+1658$ |
| 145152.1-f1 |
145152.1-f |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145152.1 |
\( 2^{8} \cdot 3^{4} \cdot 7 \) |
\( 2^{26} \cdot 3^{12} \cdot 7 \) |
$3.02103$ |
$(-2a+1), (-3a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.065326844$ |
$0.495426483$ |
4.875525635 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 801 a - 657\) , \( 8652 a - 2382\bigr] \) |
${y}^2={x}^{3}+\left(801a-657\right){x}+8652a-2382$ |
*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.
