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-a5
45.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{8} \)
$0.51752$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$7.846755528$
0.438646969
\( \frac{111284641}{50625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
225.1-b5
225.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{14} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$4.557981702$
1.019195692
\( \frac{111284641}{50625} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 49 \phi - 100\) , \( -147 \phi + 243\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(49\phi-100\right){x}-147\phi+243$
405.1-a5
405.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{20} \cdot 5^{8} \)
$0.89637$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.397318975$
0.759663617
\( \frac{111284641}{50625} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-90{x}+175$
2025.1-b5
2025.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{20} \cdot 5^{14} \)
$1.34039$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2^{4} \)
$1$
$1.169725251$
2.092468141
\( \frac{111284641}{50625} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -450 \phi - 450\) , \( -3500 \phi - 2625\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-450\phi-450\right){x}-3500\phi-2625$
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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.