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
52.1-h2
52.1-h
$2$
$7$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
52.1
\( 2^{2} \cdot 13 \)
\( 2^{26} \cdot 13^{2} \)
$1.93462$
$(2,a), (2,a+1), (13,a+6)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.6.1
$1$
\( 2 \)
$0.197635432$
$18.89430030$
1.852673694
\( -\frac{2146689}{1664} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4876 a - 22104\) , \( -560288 a + 2538732\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4876a-22104\right){x}-560288a+2538732$
52.1-i2
52.1-i
$2$
$7$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
52.1
\( 2^{2} \cdot 13 \)
\( 2^{14} \cdot 13^{2} \)
$1.93462$
$(2,a), (2,a+1), (13,a+6)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.1.1
$1$
\( 2 \cdot 7^{2} \)
$1$
$18.89430030$
4.687099046
\( -\frac{2146689}{1664} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$
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.