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-e2
45.1-e
$4$
$4$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( - 3^{17} \cdot 5 \)
$2.13379$
$(3,a), (3,a+2), (5,a+2)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$3.987782348$
$22.83873331$
2.469642019
\( \frac{7741}{135} a + \frac{264962}{135} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -5 a - 14\) , \( 15 a + 62\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-14\right){x}+15a+62$
45.1-f2
45.1-f
$4$
$4$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( - 3^{5} \cdot 5 \)
$2.13379$
$(3,a), (3,a+2), (5,a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \cdot 3 \)
$1$
$22.83873331$
3.715812656
\( \frac{7741}{135} a + \frac{264962}{135} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a - 10\) , \( a + 34\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-10\right){x}+a+34$
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Pari/GP
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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.