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
23.2-a2
23.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.70557$
$(3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.99298185$
0.900901198
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 3\) , \( 2 a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+3\right){x}+2a+2$
207.3-a2
207.3-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.3
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23 \)
$1.22209$
$(-a+1), (3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.226911519$
$23.47890425$
1.477619767
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( a - 3\) , \( -a + 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-3\right){x}-a+1$
207.5-a2
207.5-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.5
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23 \)
$1.22209$
$(-a), (3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$10.36637625$
1.437557735
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( -a - 3\) , \( a - 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a-3\right){x}+a-1$
529.2-a2
529.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
529.2
\( 23^{2} \)
\( - 23^{7} \)
$1.54516$
$(3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.326837154$
$8.479583753$
1.537319987
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 19 a - 44\) , \( -64 a + 139\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-44\right){x}-64a+139$
1863.2-g2
1863.2-g
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1863.2
\( 3^{4} \cdot 23 \)
\( - 3^{12} \cdot 23 \)
$2.11672$
$(-a), (-a+1), (3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.288317111$
$18.73250944$
2.995881965
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a - 8\) , \( -4 a + 10\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a-8\right){x}-4a+10$
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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.