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
12.2-a1
12.2-a
$2$
$2$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( 2^{4} \cdot 3^{18} \)
$1.53336$
$(3,a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.126569341$
$19.44068589$
1.601333870
\( -\frac{4133602}{729} a + \frac{34766975}{972} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3749 a - 15408\) , \( 223496 a + 918518\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3749a-15408\right){x}+223496a+918518$
12.2-a2
12.2-a
$2$
$2$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( - 2^{2} \cdot 3^{24} \)
$1.53336$
$(3,a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.253138682$
$9.720342945$
1.601333870
\( \frac{2087352478285}{531441} a + \frac{5719028825027}{354294} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -57679 a - 237048\) , \( 16063422 a + 66017006\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-57679a-237048\right){x}+16063422a+66017006$
12.2-b1
12.2-b
$2$
$2$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( 2^{4} \cdot 3^{6} \)
$1.53336$
$(3,a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$19.44068589$
2.108638445
\( -\frac{4133602}{729} a + \frac{34766975}{972} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3 a - 4\) , \( -a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-4\right){x}-a+3$
12.2-b2
12.2-b
$2$
$2$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( - 2^{2} \cdot 3^{12} \)
$1.53336$
$(3,a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$9.720342945$
2.108638445
\( \frac{2087352478285}{531441} a + \frac{5719028825027}{354294} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13 a - 44\) , \( 37 a + 161\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13a-44\right){x}+37a+161$
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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.