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-a2
31.2-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
31.2
\( 31 \)
\( -31 \)
$0.47148$
$(5a-3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.87720992$
0.359928959
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( 16 \phi - 2\) , \( -172 \phi - 94\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(16\phi-2\right){x}-172\phi-94$
775.2-a2
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
$4$
\( 2 \)
$1$
$1.686614230$
1.508553628
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[\phi + 1\) , \( -1\) , \( 0\) , \( 94 \phi - 104\) , \( 792 \phi - 255\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}-{x}^{2}+\left(94\phi-104\right){x}+792\phi-255$
961.3-c2
961.3-c
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
961.3
\( 31^{2} \)
\( - 31^{7} \)
$1.11251$
$(5a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$7.096706804$
$0.430920289$
1.367630581
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( 497 \phi - 153\) , \( -20816 \phi - 16670\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(497\phi-153\right){x}-20816\phi-16670$
2511.2-f2
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
$4$
\( 2 \)
$1$
$1.257128023$
1.124409487
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 151 \phi - 18\) , \( 4776 \phi + 2508\bigr] \)
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(151\phi-18\right){x}+4776\phi+2508$
3751.3-a2
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
$16$
\( 2 \)
$1$
$0.723404901$
2.588132054
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[1\) , \( \phi + 1\) , \( 0\) , \( 175 \phi - 76\) , \( -3463 \phi - 3142\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(175\phi-76\right){x}-3463\phi-3142$
3751.5-b2
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
$1$
\( 2^{2} \)
$1$
$6.103070773$
2.729376224
\( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 333 \phi - 486\) , \( -2737 \phi + 5677\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(333\phi-486\right){x}-2737\phi+5677$
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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.