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
100101.3-a1
100101.3-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100101.3
\( 3 \cdot 61 \cdot 547 \)
\( 3^{2} \cdot 61 \cdot 547 \)
$2.75302$
$(-2a+1), (-9a+4), (-27a+14)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.100847362$
$4.697263817$
4.375914735
\( \frac{76395909}{33367} a - \frac{46463146}{100101} \)
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -3 a + 1\) , \( -a - 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-3a+1\right){x}-a-1$
100101.3-b1
100101.3-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100101.3
\( 3 \cdot 61 \cdot 547 \)
\( 3^{12} \cdot 61 \cdot 547 \)
$2.75302$
$(-2a+1), (-9a+4), (-27a+14)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.414525973$
$1.950157769$
3.733798312
\( \frac{2121327533}{24324543} a + \frac{175921315}{900909} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2 a + 8\) , \( -11 a + 22\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2a+8\right){x}-11a+22$
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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.