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
24.1-a4
24.1-a
$6$
$8$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$0.96894$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$22.73403407$
1.160141318
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-9{x}+3$
24.1-b4
24.1-b
$6$
$8$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$0.96894$
$(-a+2), (a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$0.539636932$
$9.301119475$
1.024545539
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 122 a - 296\) , \( 1012 a - 2478\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(122a-296\right){x}+1012a-2478$
48.1-a4
48.1-a
$6$
$8$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
48.1
\( 2^{4} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$1.15227$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$9.301119475$
1.898583062
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -10\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}-10$
48.1-b4
48.1-b
$6$
$8$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
48.1
\( 2^{4} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$1.15227$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$22.73403407$
1.160141318
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 120 a - 297\) , \( -891 a + 2181\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(120a-297\right){x}-891a+2181$
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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.