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
26.4-a1
26.4-a
$4$
$6$
4.4.9248.1
$4$
$[4, 0]$
26.4
\( 2 \cdot 13 \)
\( - 2^{6} \cdot 13^{6} \)
$12.91321$
$(a), (a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.235921893$
$129.3290458$
3.807339941
\( \frac{13179827674651809978387}{38614472} a^{3} + \frac{28149201874182484162433}{38614472} a^{2} - \frac{5778658371471464319445}{38614472} a - \frac{12341938383390744470007}{38614472} \)
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 5 a + 1\) , \( a^{2} + a - 3\) , \( -82 a^{3} - 185 a^{2} + 21 a + 87\) , \( 1241 a^{3} + 2655 a^{2} - 538 a - 1169\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-82a^{3}-185a^{2}+21a+87\right){x}+1241a^{3}+2655a^{2}-538a-1169$
26.4-b1
26.4-b
$4$
$6$
4.4.9248.1
$4$
$[4, 0]$
26.4
\( 2 \cdot 13 \)
\( - 2^{6} \cdot 13^{6} \)
$12.91321$
$(a), (a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \cdot 3 \)
$1.048583304$
$14.24381837$
1.863745901
\( \frac{13179827674651809978387}{38614472} a^{3} + \frac{28149201874182484162433}{38614472} a^{2} - \frac{5778658371471464319445}{38614472} a - \frac{12341938383390744470007}{38614472} \)
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 1\) , \( 92 a^{3} + 43 a^{2} - 427 a - 275\) , \( 353 a^{3} + 162 a^{2} - 1654 a - 1064\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(92a^{3}+43a^{2}-427a-275\right){x}+353a^{3}+162a^{2}-1654a-1064$
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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.