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-b8
45.1-b
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{5} \)
$2.706065934$
$0.490422220$
5.932142254
\( \frac{1114544804970241}{405} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -278636 a - 1855392\) , \( -215960088 a - 1438058889\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-278636w-1855392\right){x}-215960088w-1438058889$
45.1-c8
45.1-c
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{2} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$4.300387515$
$0.490422220$
2.356789441
\( \frac{1114544804970241}{405} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
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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.