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-a1
23.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( - 23^{2} \)
$0.70557$
$(3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.496490929$
0.900901198
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 7\) , \( 10 a - 14\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-7\right){x}+10a-14$
207.3-a1
207.3-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.3
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23^{2} \)
$1.22209$
$(-a+1), (3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.113455759$
$11.73945212$
1.477619767
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( 26 a - 58\) , \( -84 a + 189\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(26a-58\right){x}-84a+189$
207.5-a1
207.5-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.5
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23^{2} \)
$1.22209$
$(-a), (3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.183188125$
1.437557735
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[a\) , \( -a\) , \( a\) , \( 9 a - 18\) , \( 24 a - 49\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(9a-18\right){x}+24a-49$
529.2-a1
529.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
529.2
\( 23^{2} \)
\( - 23^{8} \)
$1.54516$
$(3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.653674308$
$4.239791876$
1.537319987
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 309 a - 699\) , \( -3887 a + 8947\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(309a-699\right){x}-3887a+8947$
1863.2-g1
1863.2-g
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1863.2
\( 3^{4} \cdot 23 \)
\( - 3^{12} \cdot 23^{2} \)
$2.11672$
$(-a), (-a+1), (3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$0.144158555$
$9.366254723$
2.995881965
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 46 a - 98\) , \( -220 a + 532\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(46a-98\right){x}-220a+532$
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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.