| 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 |
| 450.1-a1 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.049563843$ |
$5.755368069$ |
4.658246279 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -20 a - 83\) , \( 163 a + 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-83\right){x}+163a+523$ |
| 450.1-c1 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 738 a - 1809\) , \( 17478 a - 42813\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(738a-1809\right){x}+17478a-42813$ |
| 750.1-q1 |
750.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.1 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{16} \cdot 3 \cdot 5^{13} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.365411003$ |
3.862699993 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 42 a - 153\) , \( 370 a - 705\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(42a-153\right){x}+370a-705$ |
| 750.1-w1 |
750.1-w |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.1 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{16} \cdot 3 \cdot 5^{13} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.908322278$ |
1.947673269 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1061 a - 2602\) , \( -50175 a - 122902\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-1061a-2602\right){x}-50175a-122902$ |
| 750.2-t1 |
750.2-t |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.2 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{16} \cdot 3 \cdot 5^{13} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$1.908322278$ |
3.116277231 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -184 a - 464\) , \( -3967 a - 9703\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-184a-464\right){x}-3967a-9703$ |
| 750.2-x1 |
750.2-x |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.2 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{16} \cdot 3 \cdot 5^{13} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.365411003$ |
0.965674998 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 294 a - 729\) , \( 4436 a - 10851\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(294a-729\right){x}+4436a-10851$ |
*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.
