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
45.2-a1
45.2-a
$4$
$6$
3.3.257.1
$3$
$[3, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{6} \cdot 5^{4} \)
$2.70172$
$(a^2-3), (a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$173.0488798$
1.199388060
\( \frac{266828773549}{625} a^{2} + \frac{319939354557}{625} a - \frac{363891969838}{625} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 4 a - 15\) , \( -2 a^{2} - 4 a + 19\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(4a-15\right){x}-2a^{2}-4a+19$
45.2-b1
45.2-b
$4$
$6$
3.3.257.1
$3$
$[3, 0]$
45.2
\( 3^{2} \cdot 5 \)
\( 3^{6} \cdot 5^{4} \)
$2.70172$
$(a^2-3), (a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.065907809$
$67.02863078$
1.653415156
\( \frac{266828773549}{625} a^{2} + \frac{319939354557}{625} a - \frac{363891969838}{625} \)
\( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 3\) , \( 36 a^{2} - 12 a - 156\) , \( 166 a^{2} - 48 a - 700\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-{x}^{2}+\left(36a^{2}-12a-156\right){x}+166a^{2}-48a-700$
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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.