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
55.2-a2
55.2-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
55.2
\( 5 \cdot 11 \)
\( - 5^{3} \cdot 11^{3} \)
$0.54414$
$(-2a+1), (-3a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 1 \)
$1$
$4.414905721$
0.493601465
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \)
\( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 5\) , \( -2 \phi - 15\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-5\right){x}-2\phi-15$
275.1-a2
275.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( - 5^{9} \cdot 11^{3} \)
$0.81369$
$(-2a+1), (-3a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$8.877874152$
0.992576504
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \)
\( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( 24 \phi - 1\) , \( 379 \phi + 255\bigr] \)
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(24\phi-1\right){x}+379\phi+255$
605.2-b2
605.2-b
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
605.2
\( 5 \cdot 11^{2} \)
\( - 5^{3} \cdot 11^{9} \)
$0.99097$
$(-2a+1), (-3a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$3.758787690$
1.260735718
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 65 \phi - 82\) , \( -390 \phi + 231\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(65\phi-82\right){x}-390\phi+231$
3025.2-e2
3025.2-e
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( - 5^{9} \cdot 11^{9} \)
$1.48185$
$(-2a+1), (-3a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1.277015932$
$0.947959835$
2.165515227
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 238 \phi - 87\) , \( 9419 \phi + 4486\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(238\phi-87\right){x}+9419\phi+4486$
4455.2-a2
4455.2-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4455.2
\( 3^{4} \cdot 5 \cdot 11 \)
\( - 3^{12} \cdot 5^{3} \cdot 11^{3} \)
$1.63243$
$(-2a+1), (-3a+2), (3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$6.617176699$
1.479645692
\( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \)
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 44 \phi - 47\) , \( 91 \phi + 310\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(44\phi-47\right){x}+91\phi+310$
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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.