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
12.1-a1
12.1-a
$2$
$2$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
12.1
\( 2^{2} \cdot 3 \)
\( 2^{2} \cdot 3^{8} \)
$2.38128$
$(3,a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$27.17693563$
3.796239038
\( -\frac{327111324371}{13122} a + \frac{2505380625335}{13122} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 44 a - 156\) , \( -174 a + 1800\bigr] \)
${y}^2+w{x}{y}={x}^3+\left(w+1\right){x}^2+\left(44w-156\right){x}-174w+1800$
12.1-a2
12.1-a
$2$
$2$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
12.1
\( 2^{2} \cdot 3 \)
\( 2^{4} \cdot 3^{4} \)
$2.38128$
$(3,a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$27.17693563$
3.796239038
\( -\frac{127985}{324} a + \frac{1378343}{81} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 14 a + 74\) , \( 32 a + 224\bigr] \)
${y}^2+w{x}{y}={x}^3+\left(w+1\right){x}^2+\left(14w+74\right){x}+32w+224$
12.1-b1
12.1-b
$2$
$2$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
12.1
\( 2^{2} \cdot 3 \)
\( 2^{2} \cdot 3^{8} \)
$2.38128$
$(3,a), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1.754871855$
$27.17693563$
3.330956522
\( -\frac{327111324371}{13122} a + \frac{2505380625335}{13122} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -43 a - 274\) , \( 210 a + 1385\bigr] \)
${y}^2+{x}{y}+\left(w+1\right){y}={x}^3+\left(w+1\right){x}^2+\left(-43w-274\right){x}+210w+1385$
12.1-b2
12.1-b
$2$
$2$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
12.1
\( 2^{2} \cdot 3 \)
\( 2^{4} \cdot 3^{4} \)
$2.38128$
$(3,a), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.877435927$
$27.17693563$
3.330956522
\( -\frac{127985}{324} a + \frac{1378343}{81} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -13 a - 74\) , \( -108 a - 733\bigr] \)
${y}^2+{x}{y}+\left(w+1\right){y}={x}^3+\left(w+1\right){x}^2+\left(-13w-74\right){x}-108w-733$
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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.