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-a3
9.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( - 3^{14} \)
$0.55805$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$1.712469082$
0.474953467
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 265 a - 594\) , \( 3141 a - 7218\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(265a-594\right){x}+3141a-7218$
27.1-a3
27.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.1
\( 3^{3} \)
\( - 3^{20} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{4} \)
$1$
$0.783192375$
0.868873929
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 464 a - 989\) , \( 6420 a - 15050\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(464a-989\right){x}+6420a-15050$
27.2-a3
27.2-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.2
\( 3^{3} \)
\( - 3^{20} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1$
$4.699154254$
0.868873929
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \)
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 849 a + 1064\) , \( 21278 a + 27823\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(849a+1064\right){x}+21278a+27823$
81.1-a3
81.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( - 3^{26} \)
$0.96657$
$(-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$2.149143493$
1.192130317
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 2381 a - 5352\) , \( -81841 a + 187736\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2381a-5352\right){x}-81841a+187736$
1521.1-h3
1521.1-h
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( - 3^{14} \cdot 13^{6} \)
$2.01207$
$(-a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$1.788195475$
0.991912381
\( -\frac{16961124145384625}{6561} a + \frac{13019221158502750}{2187} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 899 a + 52\) , \( -14940 a - 5427\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(899a+52\right){x}-14940a-5427$
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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.