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
118857.1-a1
118857.1-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
118857.1
\( 3 \cdot 39619 \)
\( 3^{2} \cdot 39619 \)
$2.87379$
$(-2a+1), (-207a+190)$
$3$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.051739241$
$4.731148459$
4.522473041
\( -\frac{25579250}{118857} a + \frac{71495307}{39619} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 1\) , \( -a\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-a$
118857.1-b1
118857.1-b
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
118857.1
\( 3 \cdot 39619 \)
\( 3^{4} \cdot 39619^{3} \)
$2.87379$
$(-2a+1), (-207a+190)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 2^{2} \cdot 3 \)
$1.966374892$
$0.631568788$
3.824063370
\( -\frac{1793621554188516253}{559697076122931} a - \frac{173322006175574366}{62188564013659} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -40 a + 165\) , \( 860 a - 29\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-40a+165\right){x}+860a-29$
118857.1-b2
118857.1-b
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
118857.1
\( 3 \cdot 39619 \)
\( 3^{12} \cdot 39619 \)
$2.87379$
$(-2a+1), (-207a+190)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 2^{2} \cdot 3 \)
$0.655458297$
$1.894706366$
3.824063370
\( \frac{277174069}{1069713} a + \frac{43396648543}{28882251} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5 a - 15\) , \( -4 a - 11\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(5a-15\right){x}-4a-11$
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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.