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
980.1-a1 980.1-a $4$
$4$
\(\Q(\sqrt{5}) \) $2$
$[2, 0]$
980.1
\( 2^{2} \cdot 5 \cdot 7^{2} \)
\( 2^{8} \cdot 5^{4} \cdot 7^{2} \)
$1.11797$
$(-2a+1), (2), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{3} \)
$1$
$5.572473402$
1.246042932
\( \frac{1367631}{2800} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$
4900.1-a1 4900.1-a $4$
$4$
\(\Q(\sqrt{5}) \) $2$
$[2, 0]$
4900.1
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 5^{10} \cdot 7^{2} \)
$1.67175$
$(-2a+1), (2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$4.394590828$
1.965320765
\( \frac{1367631}{2800} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 12 \phi + 12\) , \( 55 \phi + 41\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(12\phi+12\right){x}+55\phi+41$
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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.
