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-a1
45.1-a
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{32} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$6.492249124$
0.774245886
\( \frac{4733169839}{3515625} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -35 a^{3} + 174 a^{2} - 140 a - 32\) , \( -328 a^{3} + 1241 a^{2} - 884 a - 245\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-35a^{3}+174a^{2}-140a-32\right){x}-328a^{3}+1241a^{2}-884a-245$
45.1-b10
45.1-b
$10$
$32$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{32} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{7} \)
$1$
$3.848223270$
0.917854808
\( \frac{4733169839}{3515625} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
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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.