| 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 |
| 51984.2-a1 |
51984.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
51984.2 |
\( 2^{4} \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 19^{8} \) |
$2.33704$ |
$(-2a+1), (-5a+3), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.423570388$ |
2.934581731 |
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 72 a + 264\) , \( 2016 a - 2092\bigr] \) |
${y}^2={x}^{3}+\left(72a+264\right){x}+2016a-2092$ |
| 92416.2-h1 |
92416.2-h |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
92416.2 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{8} \) |
$2.69858$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$1$ |
\( 1 \) |
$2.211706495$ |
$0.733645432$ |
3.747253515 |
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a - 88\) , \( 286 a + 237\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a-88\right){x}+286a+237$ |
| 92416.2-p1 |
92416.2-p |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
92416.2 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{8} \) |
$2.69858$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$1$ |
\( 7 \) |
$0.315958070$ |
$0.733645432$ |
3.747253515 |
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -87 a + 112\) , \( -262 a - 149\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-87a+112\right){x}-262a-149$ |
| 109744.2-b1 |
109744.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
109744.2 |
\( 2^{4} \cdot 19^{3} \) |
\( 2^{16} \cdot 19^{14} \) |
$2.81705$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.178687083$ |
$0.168309805$ |
2.917099425 |
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2231 a + 944\) , \( -22322 a + 36357\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2231a+944\right){x}-22322a+36357$ |
| 109744.3-b1 |
109744.3-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
109744.3 |
\( 2^{4} \cdot 19^{3} \) |
\( 2^{16} \cdot 19^{14} \) |
$2.81705$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$7$ |
7B |
$1$ |
\( 2 \cdot 3 \) |
$1.250809581$ |
$0.168309805$ |
2.917099425 |
\( \frac{3517118889984}{893871739} a - \frac{927876390912}{893871739} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1969 a - 1912\) , \( -36310 a + 24051\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1969a-1912\right){x}-36310a+24051$ |
*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.
