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
135.3-d1 135.3-d $2$
$3$
\(\Q(\sqrt{10}) \) $2$
$[2, 0]$
135.3
\( 3^{3} \cdot 5 \)
\( - 2^{12} \cdot 3^{5} \cdot 5^{3} \)
$1.92642$
$(3,a+2), (5,a)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B.1.1 $1$
\( 3^{2} \)
$0.367977483$
$26.85793377$
3.125315340
\( \frac{65536}{25} a - \frac{32768}{5} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 15\) , \( -5 a - 15\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-15\right){x}-5a-15$
135.3-e1 135.3-e $2$
$3$
\(\Q(\sqrt{10}) \) $2$
$[2, 0]$
135.3
\( 3^{3} \cdot 5 \)
\( - 3^{5} \cdot 5^{3} \)
$1.92642$
$(3,a+2), (5,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B $1$
\( 1 \)
$0.213751639$
$26.85793377$
1.815440639
\( \frac{65536}{25} a - \frac{32768}{5} \)
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 1\) , \( 1\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-1\right){x}+1$
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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.
