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
6.2-a1
6.2-a
$2$
$2$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
6.2
\( 2 \cdot 3 \)
\( 2^{8} \cdot 3^{6} \)
$1.89708$
$(-23a+156), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$2.855685675$
$2.174972395$
2.747302561
\( \frac{3535318439}{5832} a - \frac{47959064233}{11664} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -187 a - 1189\) , \( -9426 a - 63802\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-187a-1189\right){x}-9426a-63802$
6.2-a2
6.2-a
$2$
$2$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
6.2
\( 2 \cdot 3 \)
\( 2^{4} \cdot 3^{3} \)
$1.89708$
$(-23a+156), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \cdot 3 \)
$5.711371350$
$2.174972395$
2.747302561
\( -\frac{538476234670117}{108} a + \frac{3652123591000837}{108} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4047 a - 27369\) , \( -375214 a - 2544698\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4047a-27369\right){x}-375214a-2544698$
6.2-b1
6.2-b
$2$
$2$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
6.2
\( 2 \cdot 3 \)
\( 2^{8} \cdot 3^{6} \)
$1.89708$
$(-23a+156), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.231145592$
$23.69682198$
2.422802775
\( \frac{3535318439}{5832} a - \frac{47959064233}{11664} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2401231 a - 16285948\) , \( -5263220672 a + 35696899378\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2401231a-16285948\right){x}-5263220672a+35696899378$
6.2-b2
6.2-b
$2$
$2$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
6.2
\( 2 \cdot 3 \)
\( 2^{4} \cdot 3^{3} \)
$1.89708$
$(-23a+156), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \cdot 3 \)
$0.462291185$
$23.69682198$
2.422802775
\( -\frac{538476234670117}{108} a + \frac{3652123591000837}{108} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 38420891 a - 260583168\) , \( -337407147144 a + 2288406610602\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(38420891a-260583168\right){x}-337407147144a+2288406610602$
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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.