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
2.1-a1
2.1-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( - 2^{4} \)
$1.12963$
$(-a+6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$25.42172449$
1.195737336
\( -\frac{4825}{16} a + \frac{28021}{16} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -57 a - 264\) , \( -14594 a - 70270\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-57a-264\right){x}-14594a-70270$
16.5-a1
16.5-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( - 2^{16} \)
$1.89980$
$(-a+6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.781056439$
$10.27635668$
3.443559771
\( -\frac{4825}{16} a + \frac{28021}{16} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 109449 a - 636447\) , \( 31048831 a - 180551202\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(109449a-636447\right){x}+31048831a-180551202$
32.3-h1
32.3-h
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
32.3
\( 2^{5} \)
\( - 2^{16} \)
$2.25926$
$(-a+6), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.709658349$
$22.97376349$
3.067412879
\( -\frac{4825}{16} a + \frac{28021}{16} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 8 a + 40\) , \( 20 a + 96\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a+40\right){x}+20a+96$
64.6-a1
64.6-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
64.6
\( 2^{6} \)
\( - 2^{22} \)
$2.68672$
$(-a+6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$3.729345894$
$7.266481497$
5.098560907
\( -\frac{4825}{16} a + \frac{28021}{16} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -5454 a - 26273\) , \( -13921058 a - 67030915\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5454a-26273\right){x}-13921058a-67030915$
64.6-d1
64.6-d
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
64.6
\( 2^{6} \)
\( - 2^{22} \)
$2.68672$
$(-a+6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.987936888$
0.845513979
\( -\frac{4825}{16} a + \frac{28021}{16} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 6 a - 28\) , \( a + 8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(6a-28\right){x}+a+8$
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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.