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
8.1-a1 8.1-a $2$
$7$
3.3.169.1 $3$
$[3, 0]$
8.1
\( 2^{3} \)
\( - 2^{42} \)
$1.64285$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$7$
7B.1.3 $1$
\( 2 \cdot 7 \)
$1$
$0.559664806$
0.602715945
\( -\frac{38575685889}{16384} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 2\) , \( 149 a^{2} - 150 a - 657\) , \( 1719 a^{2} - 1999 a - 6787\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(149a^{2}-150a-657\right){x}+1719a^{2}-1999a-6787$
8.1-a2 8.1-a $2$
$7$
3.3.169.1 $3$
$[3, 0]$
8.1
\( 2^{3} \)
\( - 2^{6} \)
$1.64285$
$(2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$7$
7B.1.1 $1$
\( 2 \)
$1$
$191.9650286$
0.602715945
\( \frac{351}{4} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 2\) , \( -a^{2} + 3\) , \( -a^{2} + a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{2}+3\right){x}-a^{2}+a+3$
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Pari/GP
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Magma
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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.
