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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 7920.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.v1 | 7920b1 | \([0, 0, 0, -267, 1674]\) | \(76136652/275\) | \(7603200\) | \([2]\) | \(2560\) | \(0.18145\) | \(\Gamma_0(N)\)-optimal |
7920.v2 | 7920b2 | \([0, 0, 0, -147, 3186]\) | \(-6353046/75625\) | \(-4181760000\) | \([2]\) | \(5120\) | \(0.52802\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.v have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.v do not have complex multiplication.Modular form 7920.2.a.v
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.