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
70189.2-a1
70189.2-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
70189.2
\( 7 \cdot 37 \cdot 271 \)
\( 7^{6} \cdot 37^{3} \cdot 271 \)
$2.51922$
$(-3a+1), (-7a+4), (-19a+9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 2 \cdot 3^{2} \)
$1$
$1.297578784$
2.996629842
\( -\frac{2345020919078517}{1614963469987} a + \frac{108055978485787}{1614963469987} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 19 a + 9\) , \( -53 a + 74\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(19a+9\right){x}-53a+74$
70189.2-a2
70189.2-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
70189.2
\( 7 \cdot 37 \cdot 271 \)
\( 7^{2} \cdot 37 \cdot 271^{3} \)
$2.51922$
$(-3a+1), (-7a+4), (-19a+9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$9$
\( 2 \cdot 3 \)
$1$
$0.432526261$
2.996629842
\( -\frac{195586795962737672425}{36083252443} a + \frac{265888440696118257954}{36083252443} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 1579 a + 994\) , \( -26239 a + 47053\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(1579a+994\right){x}-26239a+47053$
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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.