| 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 |
| 225.1-a2 |
225.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{10} \) |
$0.77387$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.1.4[2] |
$1$ |
\( 1 \) |
$1$ |
$1.950256996$ |
0.872181443 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( \phi\) , \( 1\) , \( -8 \phi + 17\) , \( 76 \phi - 131\bigr] \) |
${y}^2+{y}={x}^{3}+\phi{x}^{2}+\left(-8\phi+17\right){x}+76\phi-131$ |
| 225.1-c2 |
225.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{4} \) |
$0.77387$ |
$(-2a+1), (3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.1[2] |
$1$ |
\( 5 \) |
$1$ |
$9.835591419$ |
0.879722040 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$ |
| 2025.1-a2 |
2025.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.127940452$ |
$1.453635739$ |
1.996134097 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 15\) , \( -99\bigr] \) |
${y}^2+{y}={x}^{3}+15{x}-99$ |
| 2025.1-f2 |
2025.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2025.1 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{10} \) |
$1.34039$ |
$(-2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1.466203400$ |
1.311412189 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -75 \phi + 150\) , \( -1975 \phi + 3456\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-75\phi+150\right){x}-1975\phi+3456$ |
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*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.
