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
81.1-a1 81.1-a $4$
$267$
\(\Q(\sqrt{89}) \) $2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{6} \)
$2.52903$
$(3)$
0
$\Z/3\Z$
$\textsf{potential}$
$-267$
$N(\mathrm{U}(1))$ ✓
✓
$3$
3B.1.1 $25$
\( 2 \)
$1$
$1.241461604$
0.731081482
\( -2086403563729465344000 a - 8798344145175011328000 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1590 a - 8580\) , \( 92750 a + 359875\bigr] \) ${y}^2+{y}={x}^{3}+\left(-1590a-8580\right){x}+92750a+359875$
81.1-a2 81.1-a $4$
$267$
\(\Q(\sqrt{89}) \) $2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{18} \)
$2.52903$
$(3)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-267$
$N(\mathrm{U}(1))$ ✓
✓
$3$
3B.1.2 $25$
\( 2 \)
$1$
$0.137940178$
0.731081482
\( -2086403563729465344000 a - 8798344145175011328000 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -14310 a - 77220\) , \( -2504250 a - 9716632\bigr] \) ${y}^2+{y}={x}^{3}+\left(-14310a-77220\right){x}-2504250a-9716632$
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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.
