| 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-a4 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.198255373$ |
$1.438842017$ |
4.658246279 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -8240 a - 19943\) , \( 627019 a + 1535299\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8240a-19943\right){x}+627019a+1535299$ |
| 450.1-c4 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.326793935$ |
1.067304524 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4842 a + 11451\) , \( -67614 a + 162495\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4842a+11451\right){x}-67614a+162495$ |
| 750.1-q4 |
750.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.1 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{4} \cdot 3^{4} \cdot 5^{19} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.182705501$ |
3.862699993 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3618 a - 7213\) , \( 155662 a + 387467\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3618a-7213\right){x}+155662a+387467$ |
| 750.1-w4 |
750.1-w |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.1 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{4} \cdot 3^{4} \cdot 5^{19} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$1$ |
$0.238540284$ |
1.947673269 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -33020 a + 80720\) , \( 1189375 a - 2914318\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-33020a+80720\right){x}+1189375a-2914318$ |
| 750.2-t4 |
750.2-t |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.2 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{4} \cdot 3^{4} \cdot 5^{19} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.238540284$ |
3.116277231 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -56804 a - 139044\) , \( -11603147 a - 28421823\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-56804a-139044\right){x}-11603147a-28421823$ |
| 750.2-x4 |
750.2-x |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
750.2 |
\( 2 \cdot 3 \cdot 5^{3} \) |
\( - 2^{4} \cdot 3^{4} \cdot 5^{19} \) |
$2.29092$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.182705501$ |
0.965674998 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2486 a + 3251\) , \( -5344 a + 70129\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2486a+3251\right){x}-5344a+70129$ |
*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.
