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-a6
9.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{16} \)
$0.55805$
$(-a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$1$
$6.849876328$
0.474953467
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 15 a - 39\) , \( 54 a - 117\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-39\right){x}+54a-117$
27.1-a6
27.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.1
\( 3^{3} \)
\( 3^{22} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{4} \)
$1$
$3.132769503$
0.868873929
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 19 a - 74\) , \( 70 a - 224\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(19a-74\right){x}+70a-224$
27.2-a6
27.2-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
27.2
\( 3^{3} \)
\( 3^{22} \)
$0.73443$
$(-a), (-a+1)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{4} \cdot 3 \)
$1$
$9.398308509$
0.868873929
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 82 a - 204\) , \( -547 a + 1264\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(82a-204\right){x}-547a+1264$
81.1-a6
81.1-a
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{28} \)
$0.96657$
$(-a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{4} \)
$1$
$4.298286986$
1.192130317
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 131 a - 357\) , \( -1237 a + 2759\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(131a-357\right){x}-1237a+2759$
1521.1-h6
1521.1-h
$12$
$24$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{16} \cdot 13^{6} \)
$2.01207$
$(-a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{4} \)
$1$
$3.576390951$
0.991912381
\( -\frac{449577713875}{531441} a + \frac{1037190880375}{531441} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -206 a - 338\) , \( -2135 a - 2580\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-206a-338\right){x}-2135a-2580$
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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.