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-a7
9.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{26} \)
$0.55805$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$1.712469082$
0.474953467
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a - 44\) , \( 51 a - 168\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-44\right){x}+51a-168$
27.1-a7
27.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.1
\( 3^{3} \)
\( - 3^{32} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$1$
$1.566384751$
0.868873929
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -26 a - 119\) , \( 340 a + 10\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a-119\right){x}+340a+10$
27.2-a7
27.2-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.2
\( 3^{3} \)
\( - 3^{32} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{4} \cdot 3 \)
$1$
$2.349577127$
0.868873929
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 57 a - 194\) , \( -767 a + 1595\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(57a-194\right){x}-767a+1595$
81.1-a7
81.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( - 3^{38} \)
$0.96657$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$2.149143493$
1.192130317
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 41 a - 402\) , \( -1021 a + 4406\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(41a-402\right){x}-1021a+4406$
1521.1-h7
1521.1-h
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( - 3^{26} \cdot 13^{6} \)
$2.01207$
$(-a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$1.788195475$
0.991912381
\( \frac{1794398270320625}{282429536481} a + \frac{2024459751037750}{282429536481} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1311 a - 1768\) , \( 32250 a + 42283\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1311a-1768\right){x}+32250a+42283$
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Pari/GP
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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.