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
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{16} \cdot 5^{16} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$103.8759859$
0.774245886
\( \frac{111284641}{50625} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 10 a^{3} - 51 a^{2} + 40 a + 13\) , \( -49 a^{3} + 125 a^{2} - 65 a - 20\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(10a^{3}-51a^{2}+40a+13\right){x}-49a^{3}+125a^{2}-65a-20$
45.1-b7
45.1-b
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{16} \cdot 5^{16} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{7} \)
$1$
$61.57157232$
0.917854808
\( \frac{111284641}{50625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
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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.