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
31.2-a3
31.2-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
31.2
\( 31 \)
\( -31 \)
$0.47148$
$(5a-3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$51.50883971$
0.359928959
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[1\) , \( -\phi - 1\) , \( \phi\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}$
775.2-a3
775.2-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
775.2
\( 5^{2} \cdot 31 \)
\( - 5^{6} \cdot 31 \)
$1.05426$
$(-2a+1), (5a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$6.746456922$
1.508553628
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[\phi\) , \( \phi + 1\) , \( \phi\) , \( 2 \phi - 3\) , \( \phi - 4\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(2\phi-3\right){x}+\phi-4$
961.3-c3
961.3-c
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
961.3
\( 31^{2} \)
\( - 31^{7} \)
$1.11251$
$(5a-3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.774176701$
$3.447362312$
1.367630581
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[\phi\) , \( 0\) , \( 0\) , \( -7 \phi - 16\) , \( 24 \phi - 4\bigr] \)
${y}^2+\phi{x}{y}={x}^{3}+\left(-7\phi-16\right){x}+24\phi-4$
2511.2-f3
2511.2-f
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2511.2
\( 3^{4} \cdot 31 \)
\( - 3^{12} \cdot 31 \)
$1.41444$
$(5a-3), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$5.028512095$
1.124409487
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 \phi - 5\) , \( -2 \phi - 3\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3\phi-5\right){x}-2\phi-3$
3751.3-a3
3751.3-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3751.3
\( 11^{2} \cdot 31 \)
\( - 11^{6} \cdot 31 \)
$1.56372$
$(-3a+2), (5a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.787239209$
2.588132054
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( 0\) , \( -2 \phi - 5\) , \( 5 \phi - 4\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-2\phi-5\right){x}+5\phi-4$
3751.5-b3
3751.5-b
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3751.5
\( 11^{2} \cdot 31 \)
\( - 11^{6} \cdot 31 \)
$1.56372$
$(-3a+1), (5a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$12.20614154$
2.729376224
\( \frac{106208}{31} a - \frac{54753}{31} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( -7 \phi - 6\) , \( -13 \phi - 5\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-7\phi-6\right){x}-13\phi-5$
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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.