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
7.1-a1 7.1-a $4$
$6$
4.4.1957.1 $4$
$[4, 0]$
7.1
\( 7 \)
\( - 7^{6} \)
$5.04163$
$(a^2-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$1$
$79.35083879$
0.896863012
\( \frac{443958861593546408990}{117649} a^{3} + \frac{915220682926034165096}{117649} a^{2} + \frac{110890939600298461445}{117649} a - \frac{215357317054416491281}{117649} \)
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{2} - a - 1\) , \( 32 a^{3} - 57 a^{2} - 33 a + 17\) , \( 204 a^{3} - 364 a^{2} - 182 a + 118\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(32a^{3}-57a^{2}-33a+17\right){x}+204a^{3}-364a^{2}-182a+118$
7.1-a2 7.1-a $4$
$6$
4.4.1957.1 $4$
$[4, 0]$
7.1
\( 7 \)
\( -7 \)
$5.04163$
$(a^2-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 1 \)
$1$
$158.7016775$
0.896863012
\( \frac{124820}{7} a^{3} - \frac{238513}{7} a^{2} - \frac{74080}{7} a + \frac{71744}{7} \)
\( \bigl[-a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 3 a\) , \( -a^{3} + a^{2} + a\bigr] \) ${y}^2+\left(-a^{3}+a^{2}+3a\right){x}{y}+\left(-a^{3}+a^{2}+3a-1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(a^{2}-3a\right){x}-a^{3}+a^{2}+a$
7.1-a3 7.1-a $4$
$6$
4.4.1957.1 $4$
$[4, 0]$
7.1
\( 7 \)
\( - 7^{2} \)
$5.04163$
$(a^2-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$1$
$79.35083879$
0.896863012
\( -\frac{170631953648}{49} a^{3} + \frac{301490635046}{49} a^{2} + \frac{150363436017}{49} a - \frac{96330872074}{49} \)
\( \bigl[-a^{3} + a^{2} + 3 a\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( -5 a^{3} - 4 a^{2} + 7 a + 5\) , \( -6 a^{3} - 8 a^{2} - 3\bigr] \) ${y}^2+\left(-a^{3}+a^{2}+3a\right){x}{y}+\left(-a^{3}+a^{2}+3a-1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-5a^{3}-4a^{2}+7a+5\right){x}-6a^{3}-8a^{2}-3$
7.1-a4 7.1-a $4$
$6$
4.4.1957.1 $4$
$[4, 0]$
7.1
\( 7 \)
\( - 7^{3} \)
$5.04163$
$(a^2-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 1 \)
$1$
$158.7016775$
0.896863012
\( -\frac{9690935416}{343} a^{3} - \frac{12215671997}{343} a^{2} + \frac{16657874830}{343} a + \frac{14201869411}{343} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{3} - 3 a\) , \( -a^{3} - 4 a^{2} - 6 a + 1\) , \( -5 a^{3} - 11 a^{2} - a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-a^{3}-4a^{2}-6a+1\right){x}-5a^{3}-11a^{2}-a+3$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
