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-a2
12.2-a
$2$
$2$
4.4.18097.1
$4$
$[4, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( 2^{2} \cdot 3 \)
$16.39984$
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$1084.474763$
2.015376386
\( -\frac{805445}{6} a^{3} - 32672 a^{2} + \frac{4411588}{3} a + \frac{5572375}{3} \)
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + 2 a^{2} - 14 a - 8\) , \( -7 a^{3} + 36 a + 15\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(a^{3}+2a^{2}-14a-8\right){x}-7a^{3}+36a+15$
12.2-b2
12.2-b
$2$
$2$
4.4.18097.1
$4$
$[4, 0]$
12.2
\( 2^{2} \cdot 3 \)
\( 2^{2} \cdot 3 \)
$16.39984$
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$1158.817340$
2.153533842
\( -\frac{805445}{6} a^{3} - 32672 a^{2} + \frac{4411588}{3} a + \frac{5572375}{3} \)
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( a + 1\) , \( -43 a^{3} - 62 a^{2} + 133 a + 49\) , \( \frac{781}{2} a^{3} + \frac{1245}{2} a^{2} - \frac{2273}{2} a - 626\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(-43a^{3}-62a^{2}+133a+49\right){x}+\frac{781}{2}a^{3}+\frac{1245}{2}a^{2}-\frac{2273}{2}a-626$
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Pari/GP
SageMath
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.