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
361.1-a1
361.1-a
$3$
$9$
\(\Q(\sqrt{41}) \)
$2$
$[2, 0]$
361.1
\( 19^{2} \)
\( 19^{2} \)
$2.49406$
$(19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$60.32974189$
$0.205438503$
3.871251420
\( -\frac{50357871050752}{19} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$
361.1-a2
361.1-a
$3$
$9$
\(\Q(\sqrt{41}) \)
$2$
$[2, 0]$
361.1
\( 19^{2} \)
\( 19^{6} \)
$2.49406$
$(19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$20.10991396$
$1.848946532$
3.871251420
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$
361.1-a3
361.1-a
$3$
$9$
\(\Q(\sqrt{41}) \)
$2$
$[2, 0]$
361.1
\( 19^{2} \)
\( 19^{2} \)
$2.49406$
$(19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$6.703304654$
$16.64051879$
3.871251420
\( \frac{32768}{19} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
361.1-b1
361.1-b
$1$
$1$
\(\Q(\sqrt{41}) \)
$2$
$[2, 0]$
361.1
\( 19^{2} \)
\( 19^{2} \)
$2.49406$
$(19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$6.620574626$
1.033960045
\( -\frac{32768}{19} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 427 a - 1576\) , \( 12529 a - 46379\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(427a-1576\right){x}+12529a-46379$
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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.