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
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$0.71487$
$(a)$
0
$\Z/2\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$8.973175814$
0.793124183
\( -18473000 a + 26125000 \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2 a + 2\) , \( -3 a - 5\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+2\right){x}-3a-5$
64.1-a2
64.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$0.71487$
$(a)$
0
$\Z/4\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$35.89270325$
0.793124183
\( -18473000 a + 26125000 \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 2\) , \( 3 a + 5\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(2a+2\right){x}+3a+5$
64.1-a3
64.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$0.71487$
$(a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$17.94635162$
0.793124183
\( 8000 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( -4 a - 6\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-4\right){x}-4a-6$
64.1-a4
64.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$0.71487$
$(a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$35.89270325$
0.793124183
\( 8000 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 4 a + 6\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-4\right){x}+4a+6$
64.1-a5
64.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$0.71487$
$(a)$
0
$\Z/2\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$8.973175814$
0.793124183
\( 18473000 a + 26125000 \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -2 a + 2\) , \( 3 a - 5\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+2\right){x}+3a-5$
64.1-a6
64.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$0.71487$
$(a)$
0
$\Z/4\Z$
$\textsf{potential}$
$-32$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$35.89270325$
0.793124183
\( 18473000 a + 26125000 \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -2 a + 2\) , \( -3 a + 5\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-2a+2\right){x}-3a+5$
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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.