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-c1 135.3-c $1$
$1$
\(\Q(\sqrt{10}) \) $2$
$[2, 0]$
135.3
\( 3^{3} \cdot 5 \)
\( 2^{12} \cdot 3^{3} \cdot 5^{5} \)
$1.92642$
$(3,a+2), (5,a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 1 \)
$1$
$3.001237458$
0.474537308
\( -\frac{174958978321}{125} a - \frac{110653848799}{25} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( 11 a - 98\) , \( -118 a + 193\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(11a-98\right){x}-118a+193$
135.3-f1 135.3-f $1$
$1$
\(\Q(\sqrt{10}) \) $2$
$[2, 0]$
135.3
\( 3^{3} \cdot 5 \)
\( 3^{3} \cdot 5^{5} \)
$1.92642$
$(3,a+2), (5,a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 5 \)
$1$
$3.001237458$
2.372686542
\( -\frac{174958978321}{125} a - \frac{110653848799}{25} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 4 a - 22\) , \( -27 a + 41\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-22\right){x}-27a+41$
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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.
