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
$2$
$2$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$1.33740$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3Ns
$1$
\( 2 \)
$1$
$13.97585329$
1.320594006
\( -64 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 40\) , \( -286 a + 756\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(16a-40\right){x}-286a+756$
64.1-a2
64.1-a
$2$
$2$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.33740$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3Ns
$1$
\( 1 \)
$1$
$27.95170658$
1.320594006
\( 238328 \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -3\) , \( -a - 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-3{x}-a-3$
64.1-b1
64.1-b
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$1.33740$
$(a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.747220376$
$27.50074327$
1.941708926
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}$
64.1-b2
64.1-b
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$1.33740$
$(a+3)$
$1$
$\Z/4\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$1.494440753$
$13.75037163$
1.941708926
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 127\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-48a+127\right){x}$
64.1-b3
64.1-b
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.33740$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1.494440753$
$13.75037163$
1.941708926
\( 287496 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 134 a - 345\) , \( 1298 a - 3425\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(134a-345\right){x}+1298a-3425$
64.1-b4
64.1-b
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.33740$
$(a+3)$
$1$
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1.494440753$
$55.00148654$
1.941708926
\( 287496 \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 135 a - 341\) , \( -1379 a + 3661\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(135a-341\right){x}-1379a+3661$
64.1-c1
64.1-c
$2$
$2$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{12} \)
$1.33740$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3Ns
$1$
\( 2 \)
$1$
$13.97585329$
1.320594006
\( -64 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -16 a - 40\) , \( 286 a + 756\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-16a-40\right){x}+286a+756$
64.1-c2
64.1-c
$2$
$2$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.33740$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3Ns
$1$
\( 1 \)
$1$
$27.95170658$
1.320594006
\( 238328 \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 3\) , \( -3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-3\right){x}-3$
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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.