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
121.1-a2
121.1-a
$3$
$25$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 2^{12} \cdot 11^{10} \)
$2.29568$
$(a+2), (a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 1 \)
$1$
$8.512583687$
1.098969828
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 330 a - 1276\) , \( -12208 a + 47282\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(330a-1276\right){x}-12208a+47282$
121.1-b2
121.1-b
$3$
$25$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 2^{12} \cdot 11^{10} \)
$2.29568$
$(a+2), (a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.3
$1$
\( 5^{2} \)
$1$
$1.610892258$
5.199132406
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 330 a - 1276\) , \( 12208 a - 47282\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(330a-1276\right){x}+12208a-47282$
121.1-c2
121.1-c
$3$
$25$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.29568$
$(a+2), (a-2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 5^{2} \)
$1$
$1.610892258$
0.207965296
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-d2
121.1-d
$3$
$25$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.29568$
$(a+2), (a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 1 \)
$1$
$8.512583687$
1.098969828
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 16\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}-10{x}+16$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.