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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 259920.gv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.gv1 | 259920gv2 | \([0, 0, 0, -15144672, -16891686736]\) | \(7575076864/1953125\) | \(99048139655112000000000\) | \([]\) | \(24820992\) | \(3.1218\) | |
259920.gv2 | 259920gv1 | \([0, 0, 0, -5267712, 4651938416]\) | \(318767104/125\) | \(6339080937927168000\) | \([]\) | \(8273664\) | \(2.5724\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.gv have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.gv do not have complex multiplication.Modular form 259920.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.