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
79.2-a1
79.2-a
$4$
$4$
4.4.725.1
$4$
$[4, 0]$
79.2
\( 79 \)
\( 79 \)
$4.15443$
$(-3a^3+4a^2+5a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$85.17637350$
0.790842774
\( \frac{1229289972961243463386}{79} a^{3} - \frac{1815980901112985212969}{79} a^{2} - \frac{2821174880411485473637}{79} a + \frac{2575723886432473683491}{79} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -195 a^{3} + 234 a^{2} + 421 a - 359\) , \( -1610 a^{3} + 2626 a^{2} + 3852 a - 3624\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-195a^{3}+234a^{2}+421a-359\right){x}-1610a^{3}+2626a^{2}+3852a-3624$
79.2-a2
79.2-a
$4$
$4$
4.4.725.1
$4$
$[4, 0]$
79.2
\( 79 \)
\( 79^{2} \)
$4.15443$
$(-3a^3+4a^2+5a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$170.3527470$
0.790842774
\( \frac{14851548187691}{6241} a^{3} - \frac{21933749080646}{6241} a^{2} - \frac{34100233549511}{6241} a + \frac{31127365917936}{6241} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -10 a^{3} + 9 a^{2} + 26 a - 19\) , \( -34 a^{3} + 49 a^{2} + 83 a - 74\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-10a^{3}+9a^{2}+26a-19\right){x}-34a^{3}+49a^{2}+83a-74$
79.2-a3
79.2-a
$4$
$4$
4.4.725.1
$4$
$[4, 0]$
79.2
\( 79 \)
\( -79 \)
$4.15443$
$(-3a^3+4a^2+5a-2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$340.7054940$
0.790842774
\( \frac{2360876}{79} a^{3} - \frac{3521873}{79} a^{2} - \frac{5348385}{79} a + \frac{4952074}{79} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -a^{2} + a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-a^{2}+a+1\right){x}-a^{3}+a^{2}+3a-2$
79.2-a4
79.2-a
$4$
$4$
4.4.725.1
$4$
$[4, 0]$
79.2
\( 79 \)
\( - 79^{4} \)
$4.15443$
$(-3a^3+4a^2+5a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$10.64704668$
0.790842774
\( -\frac{279241381882508193670}{38950081} a^{3} + \frac{657801318853926878023}{38950081} a^{2} - \frac{54040079769760388021}{38950081} a - \frac{205979274419354339293}{38950081} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( 15 a^{3} - 56 a^{2} + 31 a + 1\) , \( 90 a^{3} - 276 a^{2} + 114 a + 28\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(15a^{3}-56a^{2}+31a+1\right){x}+90a^{3}-276a^{2}+114a+28$
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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.