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
1377.2-a1
1377.2-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1377.2
\( 3^{4} \cdot 17 \)
\( 3^{12} \cdot 17 \)
$3.96287$
$(a-6), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$4.341391037$
$11.30320686$
6.740508277
\( \frac{34263}{17} a + \frac{138726}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 38\) , \( -9 a + 37\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(9a-38\right){x}-9a+37$
1377.2-a2
1377.2-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1377.2
\( 3^{4} \cdot 17 \)
\( - 3^{12} \cdot 17^{2} \)
$3.96287$
$(a-6), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$8.682782074$
$2.825801715$
6.740508277
\( \frac{9844754985}{289} a + \frac{30913542459}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -36 a + 142\) , \( -45 a + 181\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-36a+142\right){x}-45a+181$
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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.