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
64.1-a1
64.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$0.87554$
$(a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$27.50074327$
0.992347595
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}$
64.1-a2
64.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$0.87554$
$(a+1)$
0
$\Z/4\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$1$
$13.75037163$
0.992347595
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 7\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-4a+7\right){x}$
64.1-a3
64.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$0.87554$
$(a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$13.75037163$
0.992347595
\( 287496 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a - 17\) , \( 17 a - 29\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(11a-17\right){x}+17a-29$
64.1-a4
64.1-a
$4$
$4$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$0.87554$
$(a+1)$
0
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$55.00148654$
0.992347595
\( 287496 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 10 a - 19\) , \( -36 a + 61\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-19\right){x}-36a+61$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.