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
116.1-a1
116.1-a
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
116.1
\( 2^{2} \cdot 29 \)
\( 2^{2} \cdot 29 \)
$0.65575$
$(a+5), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1[2]
$1$
\( 1 \)
$1$
$38.20407601$
0.683415287
\( -\frac{215055}{58} a - \frac{65799}{29} \)
\( \bigl[1\) , \( -1\) , \( \phi\) , \( -\phi\) , \( 0\bigr] \)
${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}-\phi{x}$
116.1-a2
116.1-a
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
116.1
\( 2^{2} \cdot 29 \)
\( 2^{10} \cdot 29^{5} \)
$0.65575$
$(a+5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.4[2]
$1$
\( 1 \)
$1$
$1.528163040$
0.683415287
\( \frac{5863892358339}{656356768} a - \frac{9487976032305}{656356768} \)
\( \bigl[1\) , \( -1\) , \( \phi\) , \( 9 \phi - 15\) , \( \phi - 33\bigr] \)
${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}+\left(9\phi-15\right){x}+\phi-33$
116.1-b1
116.1-b
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
116.1
\( 2^{2} \cdot 29 \)
\( 2^{2} \cdot 29^{7} \)
$0.65575$
$(a+5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.3
$1$
\( 7 \)
$1$
$0.227312153$
0.711599598
\( \frac{10275514224882981619}{34499752618} a - \frac{17178221996613932625}{34499752618} \)
\( \bigl[1\) , \( \phi - 1\) , \( \phi + 1\) , \( 488 \phi - 1077\) , \( 7662 \phi - 14347\bigr] \)
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(488\phi-1077\right){x}+7662\phi-14347$
116.1-b2
116.1-b
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
116.1
\( 2^{2} \cdot 29 \)
\( 2^{14} \cdot 29 \)
$0.65575$
$(a+5), (2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 7 \)
$1$
$11.13829551$
0.711599598
\( -\frac{1802653}{3712} a + \frac{4760167}{3712} \)
\( \bigl[1\) , \( \phi - 1\) , \( \phi + 1\) , \( -2 \phi + 3\) , \( -1\bigr] \)
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-2\phi+3\right){x}-1$
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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.