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 $1$
$1$
\(\Q(\sqrt{-13}) \) $2$
$[0, 1]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.82257$
$(2,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cn $1$
\( 1 \)
$1$
$7.681576726$
2.130486058
\( -74088 \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -4 a + 1\) , \( 10\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+1\right){x}+10$
64.1-c1 64.1-c $1$
$1$
\(\Q(\sqrt{-13}) \) $2$
$[0, 1]$
64.1
\( 2^{6} \)
\( 2^{6} \)
$1.82257$
$(2,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cn $1$
\( 1 \)
$1$
$7.681576726$
2.130486058
\( -74088 \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -3 a - 5\) , \( a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-3a-5\right){x}+a+7$
256.1-b1 256.1-b $1$
$1$
\(\Q(\sqrt{-13}) \) $2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{18} \)
$2.57751$
$(2,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cn $1$
\( 2 \)
$1$
$3.840788363$
2.130486058
\( -74088 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7\) , \( -2 a\bigr] \) ${y}^2={x}^3+7{x}-2a$
256.1-d1 256.1-d $1$
$1$
\(\Q(\sqrt{-13}) \) $2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{18} \)
$2.57751$
$(2,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cn $1$
\( 2 \)
$1$
$3.840788363$
2.130486058
\( -74088 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 7\) , \( 2 a\bigr] \) ${y}^2={x}^3+7{x}+2a$
Download
displayed columns for
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.
