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
648.1-a1
648.1-a
$1$
$1$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( 2^{10} \cdot 3^{10} \)
$1.56179$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2 \)
$1$
$3.432708667$
1.981875273
\( -6 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a - 5\) , \( 61 a - 107\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-5\right){x}+61a-107$
648.1-b1
648.1-b
$1$
$1$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{10} \)
$1.56179$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2 \)
$1$
$3.183550107$
1.838023511
\( -3072 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 12 a - 21\) , \( 37 a - 66\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(12a-21\right){x}+37a-66$
648.1-c1
648.1-c
$1$
$1$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{10} \)
$1.56179$
$(a+1), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2 \cdot 3 \)
$0.031242123$
$21.86689559$
2.366564274
\( -3072 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 12 a - 21\) , \( -38 a + 64\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(12a-21\right){x}-38a+64$
648.1-d1
648.1-d
$1$
$1$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( 2^{10} \cdot 3^{10} \)
$1.56179$
$(a+1), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2 \cdot 3 \)
$0.059518597$
$11.58005052$
2.387557087
\( -6 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 3 a - 3\) , \( -66 a + 115\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-3\right){x}-66a+115$
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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.