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
196.1-b6
196.1-b
$6$
$18$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{30} \cdot 7^{4} \)
$2.69562$
$(2,a), (2,a+1), (7,a+1), (7,a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3^{4} \)
$1$
$0.436190660$
4.382326219
\( \frac{2251439055699625}{25088} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 4955893 a - 22455792\) , \( 12070201777 a - 54691639792\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4955893a-22455792\right){x}+12070201777a-54691639792$
196.1-f6
196.1-f
$6$
$18$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{4} \)
$2.69562$
$(2,a), (2,a+1), (7,a+1), (7,a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$9$
\( 2^{2} \)
$1$
$0.436190660$
0.486925135
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
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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.