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
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$0.480125797$
$80.51788419$
1.708489898
\( 18473000 a^{2} - 10821000 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -2 a^{2} + 6\) , \( 3 a^{2} - 11\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-2a^{2}+6\right){x}+3a^{2}-11$
64.1-a2
64.1-a
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$0.480125797$
$80.51788419$
1.708489898
\( -18473000 a^{2} + 63071000 \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 2 a^{2} - 2\) , \( -3 a^{2} + 1\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(2a^{2}-2\right){x}-3a^{2}+1$
64.1-a3
64.1-a
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/8\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$0.240062898$
$1288.286147$
1.708489898
\( -18473000 a^{2} + 63071000 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2\) , \( 0\) , \( 2 a^{2} - 2\) , \( 3 a^{2} - 1\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(2a^{2}-2\right){x}+3a^{2}-1$
64.1-a4
64.1-a
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/8\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$0.240062898$
$1288.286147$
1.708489898
\( 18473000 a^{2} - 10821000 \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( 0\) , \( -2 a^{2} + 6\) , \( -3 a^{2} + 11\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-2a^{2}+6\right){x}-3a^{2}+11$
64.1-a5
64.1-a
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$0.240062898$
$644.1430735$
1.708489898
\( 8000 \)
\( \bigl[a^{3} - 2 a\) , \( a^{2} - 2\) , \( 0\) , \( a^{2} - 1\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{2}-1\right){x}$
64.1-a6
64.1-a
$6$
$8$
\(\Q(\zeta_{16})^+\)
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$6.80105$
$(a)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.120031449$
$2576.572294$
1.708489898
\( 8000 \)
\( \bigl[a^{3} - 2 a\) , \( a^{2} - 1\) , \( a^{3} - 2 a\) , \( a^{2} - 2\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(a^{2}-2\right){x}$
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.