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
116.2-a1
116.2-a
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
116.2
\( 2^{2} \cdot 29 \)
\( 2^{10} \cdot 29^{5} \)
$0.65575$
$(a-6), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.4[2]
$1$
\( 1 \)
$1$
$1.528163040$
0.683415287
\( -\frac{5863892358339}{656356768} a - \frac{1812041836983}{328178384} \)
\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -10 \phi - 6\) , \( -2 \phi - 32\bigr] \)
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-10\phi-6\right){x}-2\phi-32$
2900.2-n1
2900.2-n
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2900.2
\( 2^{2} \cdot 5^{2} \cdot 29 \)
\( 2^{10} \cdot 5^{6} \cdot 29^{5} \)
$1.46630$
$(-2a+1), (a-6), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.1.1[2]
$1$
\( 5^{2} \)
$1$
$3.730297850$
1.668239914
\( -\frac{5863892358339}{656356768} a - \frac{1812041836983}{328178384} \)
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -19 \phi - 9\) , \( -592 \phi + 1086\bigr] \)
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-19\phi-9\right){x}-592\phi+1086$
3364.2-h1
3364.2-h
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3364.2
\( 2^{2} \cdot 29^{2} \)
\( 2^{10} \cdot 29^{11} \)
$1.52173$
$(a-6), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1[2]
$1$
\( 2^{2} \cdot 5 \)
$0.471954673$
$0.283772752$
2.395774690
\( -\frac{5863892358339}{656356768} a - \frac{1812041836983}{328178384} \)
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -185 \phi - 106\) , \( 2351 \phi - 7433\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-185\phi-106\right){x}+2351\phi-7433$
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.