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
3721.1-a1
3721.1-a
$4$
$4$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3721.1
\( 61^{2} \)
\( - 61^{5} \)
$1.56059$
$(7a-3), (7a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$9.157674605$
2.047718293
\( -\frac{375882656589610}{13845841} a + \frac{608193773362941}{13845841} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 29 \phi - 21\) , \( 23 \phi + 116\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(29\phi-21\right){x}+23\phi+116$
3721.1-a2
3721.1-a
$4$
$4$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3721.1
\( 61^{2} \)
\( 61^{2} \)
$1.56059$
$(7a-3), (7a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$18.31534921$
2.047718293
\( \frac{456533}{61} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -\phi - 1\) , \( -3 \phi - 2\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-\phi-1\right){x}-3\phi-2$
3721.1-a3
3721.1-a
$4$
$4$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3721.1
\( 61^{2} \)
\( 61^{4} \)
$1.56059$
$(7a-3), (7a-4)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$18.31534921$
2.047718293
\( \frac{31855013}{3721} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -6 \phi - 6\) , \( 2 \phi + 3\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-6\phi-6\right){x}+2\phi+3$
3721.1-a4
3721.1-a
$4$
$4$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3721.1
\( 61^{2} \)
\( - 61^{5} \)
$1.56059$
$(7a-3), (7a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$9.157674605$
2.047718293
\( \frac{375882656589610}{13845841} a + \frac{232311116773331}{13845841} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -29 \phi + 7\) , \( -16 \phi + 103\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-29\phi+7\right){x}-16\phi+103$
3721.1-b1
3721.1-b
$1$
$1$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3721.1
\( 61^{2} \)
\( 61^{2} \)
$1.56059$
$(7a-3), (7a-4)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 1 \)
$0.029909840$
$37.61605819$
2.012622725
\( -\frac{912673}{61} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}-2{x}+1$
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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.