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
9.1-a1
9.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{4} \)
$0.55805$
$(-a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$27.39950531$
0.474953467
\( -\frac{24125}{27} a - \frac{1375}{27} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
27.1-a1
27.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.1
\( 3^{3} \)
\( 3^{10} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$6.265539006$
0.868873929
\( -\frac{24125}{27} a - \frac{1375}{27} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a + 1\) , \( -2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}-2$
27.2-a1
27.2-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.2
\( 3^{3} \)
\( 3^{10} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$18.79661701$
0.868873929
\( -\frac{24125}{27} a - \frac{1375}{27} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a + 1\) , \( -2 a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a+1\right){x}-2a+2$
81.1-a1
81.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{16} \)
$0.96657$
$(-a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{4} \)
$1$
$4.298286986$
1.192130317
\( -\frac{24125}{27} a - \frac{1375}{27} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -4 a + 3\) , \( -4 a + 5\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-4a+3\right){x}-4a+5$
1521.1-h1
1521.1-h
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{4} \cdot 13^{6} \)
$2.01207$
$(-a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$3.576390951$
0.991912381
\( -\frac{24125}{27} a - \frac{1375}{27} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11 a - 13\) , \( -55 a - 71\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-11a-13\right){x}-55a-71$
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.