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-a9
45.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$0.51752$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$0.490422220$
0.438646969
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
225.1-b9
225.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{8} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$4.557981702$
1.019195692
\( \frac{1114544804970241}{405} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -10800 \phi - 10800\) , \( 758396 \phi + 571497\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-10800\phi-10800\right){x}+758396\phi+571497$
405.1-a9
405.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( 3^{20} \cdot 5^{2} \)
$0.89637$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.397318975$
0.759663617
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-19440{x}+1048135$
2025.1-b9
2025.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{20} \cdot 5^{8} \)
$1.34039$
$(-2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$64$
\( 2^{4} \)
$1$
$0.073107828$
2.092468141
\( \frac{1114544804970241}{405} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -97200 \phi - 97200\) , \( -20962700 \phi - 15722025\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-97200\phi-97200\right){x}-20962700\phi-15722025$
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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.