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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 62400.gv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.gv1 | 62400hd2 | \([0, 1, 0, -132033, -18503937]\) | \(497169541448/190125\) | \(97344000000000\) | \([2]\) | \(368640\) | \(1.6500\) | |
62400.gv2 | 62400hd1 | \([0, 1, 0, -7033, -378937]\) | \(-601211584/609375\) | \(-39000000000000\) | \([2]\) | \(184320\) | \(1.3034\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.gv have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.gv do not have complex multiplication.Modular form 62400.2.a.gv
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.