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
55.1-a8
55.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{4} \cdot 11 \)
$0.54414$
$(-2a+1), (-3a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$19.86707574$
0.493601465
\( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \)
\( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -6 \phi - 26\) , \( 28 \phi + 8\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-6\phi-26\right){x}+28\phi+8$
275.2-a8
275.2-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{10} \cdot 11 \)
$0.81369$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$2.219468538$
0.992576504
\( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \)
\( \bigl[1\) , \( -\phi - 1\) , \( \phi + 1\) , \( 102 \phi - 228\) , \( -262 \phi + 277\bigr] \)
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(102\phi-228\right){x}-262\phi+277$
605.3-b8
605.3-b
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
605.3
\( 5 \cdot 11^{2} \)
\( 5^{4} \cdot 11^{7} \)
$0.99097$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$1.409545383$
1.260735718
\( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -140 \phi - 267\) , \( -1855 \phi - 1431\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-140\phi-267\right){x}-1855\phi-1431$
3025.3-e8
3025.3-e
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3025.3
\( 5^{2} \cdot 11^{2} \)
\( 5^{10} \cdot 11^{7} \)
$1.48185$
$(-2a+1), (-3a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.425671977$
$2.843879507$
2.165515227
\( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 637 \phi - 1975\) , \( -159 \phi + 11012\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(637\phi-1975\right){x}-159\phi+11012$
4455.1-a8
4455.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4455.1
\( 3^{4} \cdot 5 \cdot 11 \)
\( 3^{12} \cdot 5^{4} \cdot 11 \)
$1.63243$
$(-2a+1), (-3a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$1$
$1.654294174$
1.479645692
\( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -44 \phi - 227\) , \( -1090 \phi - 500\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-44\phi-227\right){x}-1090\phi-500$
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Pari/GP
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*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.