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
1.1-a3
1.1-a
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 2^{12} \)
$0.72044$
$\textsf{none}$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3Nn
$4$
\( 1 \)
$1$
$39.40181504$
1.221798417
\( 4913 \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -821 a - 2899\) , \( -23499 a - 82978\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-821a-2899\right){x}-23499a-82978$
1.1-b3
1.1-b
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.72044$
$\textsf{none}$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3Nn
$4$
\( 1 \)
$1$
$39.40181504$
0.305449604
\( 4913 \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -12 a - 35\) , \( -48 a - 174\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a-35\right){x}-48a-174$
16.4-a3
16.4-a
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{24} \)
$1.44087$
$(2,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$1$
\( 2^{2} \)
$0.977967361$
$26.09859687$
1.582904983
\( 4913 \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 139 a - 629\) , \( -1120 a + 5075\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(139a-629\right){x}-1120a+5075$
16.4-b3
16.4-b
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
16.4
\( 2^{4} \)
\( 2^{12} \)
$1.44087$
$(2,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$1$
\( 2^{2} \)
$1.496111142$
$26.09859687$
2.421555028
\( 4913 \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a - 3\) , \( -7 a - 14\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a-3\right){x}-7a-14$
16.5-a3
16.5-a
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{24} \)
$1.44087$
$(2,a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$1$
\( 2^{2} \)
$0.977967361$
$26.09859687$
1.582904983
\( 4913 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
16.5-b3
16.5-b
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{12} \)
$1.44087$
$(2,a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$1$
\( 2^{2} \)
$1.496111142$
$26.09859687$
2.421555028
\( 4913 \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 5 a - 8\) , \( 7 a - 21\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(5a-8\right){x}+7a-21$
81.1-b3
81.1-b
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 2^{12} \cdot 3^{12} \)
$2.16131$
$(3)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$1$
\( 2^{2} \)
$0.636714186$
$23.04925150$
1.820307151
\( 4913 \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7425 a - 26208\) , \( 563828 a + 1990956\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7425a-26208\right){x}+563828a+1990956$
81.1-c3
81.1-c
$6$
$8$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$2.16131$
$(3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Nn
$4$
\( 2^{2} \)
$1$
$23.04925150$
2.858907793
\( 4913 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -102 a - 360\) , \( 932 a + 3291\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-102a-360\right){x}+932a+3291$
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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.