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
136.1-A1 136.1-A $3$
$9$
3.1.23.1 $3$
$[1, 1]$
136.1
\( 2^{3} \cdot 17 \)
\( - 2^{3} \cdot 17 \)
$0.97183$
$(-a^2-2), (2)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 1 \)
$1$
$79.17989318$
0.407658000
\( -\frac{55665}{17} a^{2} + \frac{197635}{34} a - \frac{136767}{34} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
136.1-A2 136.1-A $3$
$9$
3.1.23.1 $3$
$[1, 1]$
136.1
\( 2^{3} \cdot 17 \)
\( - 2^{9} \cdot 17^{3} \)
$0.97183$
$(-a^2-2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs.1.1 $1$
\( 1 \)
$1$
$8.797765909$
0.407658000
\( \frac{214693602205}{19652} a^{2} + \frac{1064389027655}{39304} a + \frac{69858641986}{4913} \)
\( \bigl[a^{2}\) , \( -1\) , \( a^{2} + 1\) , \( -a^{2} + 26 a + 21\) , \( -88 a^{2} + 13 a + 59\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{2}+1\right){y}={x}^{3}-{x}^{2}+\left(-a^{2}+26a+21\right){x}-88a^{2}+13a+59$
136.1-A3 136.1-A $3$
$9$
3.1.23.1 $3$
$[1, 1]$
136.1
\( 2^{3} \cdot 17 \)
\( - 2^{27} \cdot 17^{9} \)
$0.97183$
$(-a^2-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $1$
\( 1 \)
$1$
$0.977529545$
0.407658000
\( -\frac{287944742921902931}{60716992766464} a^{2} + \frac{247958719176608235}{30358496383232} a - \frac{265887199961636953}{60716992766464} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -20 a^{2} - a - 30\) , \( -38 a^{2} + 36 a - 40\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a^{2}-a-30\right){x}-38a^{2}+36a-40$
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Pari/GP
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Magma
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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.
