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
45.1-a6
45.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$0.51752$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$31.38702211$
0.438646969
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
225.1-b6
225.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{10} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$4.557981702$
1.019195692
\( \frac{13997521}{225} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -25 \phi - 25\) , \( -119 \phi - 83\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-25\phi-25\right){x}-119\phi-83$
405.1-a6
405.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{16} \cdot 5^{4} \)
$0.89637$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.397318975$
0.759663617
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-45{x}-104$
2025.1-b6
2025.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{16} \cdot 5^{10} \)
$1.34039$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$4.678901004$
2.092468141
\( \frac{13997521}{225} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -225 \phi - 225\) , \( 2080 \phi + 1560\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-225\phi-225\right){x}+2080\phi+1560$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.