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-a8
45.1-a
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{16} \cdot 5^{4} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$103.8759859$
0.774245886
\( \frac{1114544804970241}{405} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 2160 a^{3} - 10801 a^{2} + 8640 a + 2163\) , \( -309839 a^{3} + 1037335 a^{2} - 687955 a - 191220\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(2160a^{3}-10801a^{2}+8640a+2163\right){x}-309839a^{3}+1037335a^{2}-687955a-191220$
45.1-b3
45.1-b
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{16} \cdot 5^{4} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$64$
\( 2^{5} \)
$1$
$0.240513954$
0.917854808
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
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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.