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
49.1-a1 49.1-a $2$
$2$
\(\Q(\sqrt{-10}) \) $2$
$[0, 1]$
49.1
\( 7^{2} \)
\( 2^{12} \cdot 7^{6} \)
$1.49526$
$(7,a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$ ✓
✓
$5$
5Nn.1.1.1 $1$
\( 2^{2} \)
$1$
$4.796364224$
1.516743543
\( 8000 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 2\) , \( -2 a - 24\bigr] \) ${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-4a+2\right){x}-2a-24$
49.1-a2 49.1-a $2$
$2$
\(\Q(\sqrt{-10}) \) $2$
$[0, 1]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.49526$
$(7,a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$ ✓
✓
$5$
5Nn.1.1.1 $1$
\( 2^{2} \)
$1$
$4.796364224$
1.516743543
\( 8000 \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( a + 7\) , \( -a + 2\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+7\right){x}-a+2$
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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.
