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
31.1-a6
31.1-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
31.1
\( 31 \)
\( -31 \)
$0.47148$
$(5a-2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.87720992$
0.359928959
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( -18 \phi + 15\) , \( 171 \phi - 265\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-18\phi+15\right){x}+171\phi-265$
775.1-a6
775.1-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
775.1
\( 5^{2} \cdot 31 \)
\( - 5^{6} \cdot 31 \)
$1.05426$
$(-2a+1), (5a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$1.686614230$
1.508553628
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[\phi\) , \( -\phi\) , \( 0\) , \( -94 \phi - 10\) , \( -792 \phi + 537\bigr] \)
${y}^2+\phi{x}{y}={x}^{3}-\phi{x}^{2}+\left(-94\phi-10\right){x}-792\phi+537$
961.2-c6
961.2-c
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
961.2
\( 31^{2} \)
\( - 31^{7} \)
$1.11251$
$(5a-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$7.096706804$
$0.430920289$
1.367630581
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[\phi\) , \( -\phi + 1\) , \( 0\) , \( -497 \phi + 344\) , \( 20816 \phi - 37486\bigr] \)
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-497\phi+344\right){x}+20816\phi-37486$
2511.1-f6
2511.1-f
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2511.1
\( 3^{4} \cdot 31 \)
\( - 3^{12} \cdot 31 \)
$1.41444$
$(5a-2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$1.257128023$
1.124409487
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -151 \phi + 133\) , \( -4927 \phi + 7417\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-151\phi+133\right){x}-4927\phi+7417$
3751.4-b6
3751.4-b
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3751.4
\( 11^{2} \cdot 31 \)
\( - 11^{6} \cdot 31 \)
$1.56372$
$(-3a+2), (5a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.103070773$
2.729376224
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -334 \phi - 152\) , \( 2250 \phi + 2607\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-334\phi-152\right){x}+2250\phi+2607$
3751.6-a6
3751.6-a
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3751.6
\( 11^{2} \cdot 31 \)
\( - 11^{6} \cdot 31 \)
$1.56372$
$(-3a+1), (5a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$16$
\( 2 \)
$1$
$0.723404901$
2.588132054
\( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \)
\( \bigl[1\) , \( -\phi - 1\) , \( 1\) , \( -173 \phi + 97\) , \( 3637 \phi - 6703\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-173\phi+97\right){x}+3637\phi-6703$
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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.