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
23.1-a2
23.1-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
23.1
\( 23 \)
\( - 23^{2} \)
$0.70557$
$(-3a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.496490929$
0.900901198
\( \frac{50955500525}{529} a + \frac{66383751309}{529} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -4 a - 4\) , \( -13 a - 18\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-4a-4\right){x}-13a-18$
207.4-a2
207.4-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.4
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23^{2} \)
$1.22209$
$(-a+1), (-3a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.183188125$
1.437557735
\( \frac{50955500525}{529} a + \frac{66383751309}{529} \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -11 a - 9\) , \( -25 a - 25\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-11a-9\right){x}-25a-25$
207.6-a2
207.6-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
207.6
\( 3^{2} \cdot 23 \)
\( - 3^{6} \cdot 23^{2} \)
$1.22209$
$(-a), (-3a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.113455759$
$11.73945212$
1.477619767
\( \frac{50955500525}{529} a + \frac{66383751309}{529} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -27 a - 32\) , \( 83 a + 105\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-32\right){x}+83a+105$
529.3-a2
529.3-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
529.3
\( 23^{2} \)
\( - 23^{8} \)
$1.54516$
$(-3a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.653674308$
$4.239791876$
1.537319987
\( \frac{50955500525}{529} a + \frac{66383751309}{529} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -307 a - 390\) , \( 3496 a + 4529\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-307a-390\right){x}+3496a+4529$
1863.1-g2
1863.1-g
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1863.1
\( 3^{4} \cdot 23 \)
\( - 3^{12} \cdot 23^{2} \)
$2.11672$
$(-a), (-a+1), (-3a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$0.144158555$
$9.366254723$
2.995881965
\( \frac{50955500525}{529} a + \frac{66383751309}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -47 a - 51\) , \( 220 a + 312\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-47a-51\right){x}+220a+312$
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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.