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
45.1-b5
45.1-b
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.353032967$
$31.38702211$
5.932142254
\( \frac{13997521}{225} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 641 a - 4888\) , \( -19640 a + 150440\bigr] \)
${y}^2+w{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(641w-4888\right){x}-19640w+150440$
45.1-c5
45.1-c
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$2.150193757$
$31.38702211$
2.356789441
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
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.