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-a4
45.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{4} \cdot 5^{16} \)
$0.51752$
$(-2a+1), (3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$1.961688882$
0.438646969
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
225.1-b4
225.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{4} \cdot 5^{22} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.139495425$
1.019195692
\( \frac{4733169839}{3515625} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 175 \phi + 175\) , \( 1081 \phi + 767\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(175\phi+175\right){x}+1081\phi+767$
405.1-a4
405.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{16} \cdot 5^{16} \)
$0.89637$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.849329743$
0.759663617
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+315{x}+1066$
2025.1-b4
2025.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{16} \cdot 5^{22} \)
$1.34039$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2^{4} \)
$1$
$0.292431312$
2.092468141
\( \frac{4733169839}{3515625} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 1575 \phi + 1575\) , \( -21320 \phi - 15990\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1575\phi+1575\right){x}-21320\phi-15990$
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Pari/GP
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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.