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
1936.1-a1
1936.1-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{6} \)
$2.13716$
$(2), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1.367533406$
$0.647455648$
4.420269990
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
${y}^2={x}^{3}+{x}^{2}-77{x}-289$
1936.1-a2
1936.1-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{2} \)
$2.13716$
$(2), (11)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 3 \)
$4.102600218$
$5.827100832$
4.420269990
\( \frac{8192}{11} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+3{x}-1$
1936.1-b1
1936.1-b
$4$
$4$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{8} \)
$2.13716$
$(2), (11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$5.211802014$
0.722746900
\( -\frac{18522000}{14641} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 105 a - 245\) , \( -1224 a + 2822\bigr] \)
${y}^2={x}^{3}+\left(105a-245\right){x}-1224a+2822$
1936.1-b2
1936.1-b
$4$
$4$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{2} \)
$2.13716$
$(2), (11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$10.42360402$
0.722746900
\( -\frac{40760629488000}{11} a + \frac{93862584594000}{11} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a - 215\) , \( 664 a + 1038\bigr] \)
${y}^2={x}^{3}+\left(-120a-215\right){x}+664a+1038$
1936.1-b3
1936.1-b
$4$
$4$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{8} \cdot 11^{4} \)
$2.13716$
$(2), (11)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$20.84720805$
0.722746900
\( \frac{442368000}{121} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 280\) , \( -972 a + 2241\bigr] \)
${y}^2={x}^{3}+\left(120a-280\right){x}-972a+2241$
1936.1-b4
1936.1-b
$4$
$4$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1936.1
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{2} \)
$2.13716$
$(2), (11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$10.42360402$
0.722746900
\( \frac{40760629488000}{11} a + \frac{53101955106000}{11} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 335\) , \( -664 a + 1702\bigr] \)
${y}^2={x}^{3}+\left(120a-335\right){x}-664a+1702$
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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.