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
36.1-a1
36.1-a
$4$
$10$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{2} \)
$0.48944$
$(2), (3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.1[2]
$1$
\( 2 \)
$1$
$44.29962169$
0.396227861
\( -\frac{24389}{12} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}$
36.1-a2
36.1-a
$4$
$10$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{10} \)
$0.48944$
$(2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.4[2]
$1$
\( 2 \)
$1$
$1.771984867$
0.396227861
\( -\frac{19465109}{248832} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -5 \phi - 5\) , \( -51 \phi - 37\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-5\phi-5\right){x}-51\phi-37$
36.1-a3
36.1-a
$4$
$10$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{10} \cdot 3^{20} \)
$0.48944$
$(2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.4[2]
$1$
\( 2 \)
$1$
$1.771984867$
0.396227861
\( \frac{502270291349}{1889568} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 165 \phi - 331\) , \( 1352 \phi - 2408\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(165\phi-331\right){x}+1352\phi-2408$
36.1-a4
36.1-a
$4$
$10$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{2} \cdot 3^{4} \)
$0.48944$
$(2), (3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.1[2]
$1$
\( 2 \)
$1$
$44.29962169$
0.396227861
\( \frac{131872229}{18} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 10 \phi - 21\) , \( -31 \phi + 51\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(10\phi-21\right){x}-31\phi+51$
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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.