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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 35280.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.v1 | 35280eg1 | \([0, 0, 0, -18963, -1005102]\) | \(-5154200289/20\) | \(-2926264320\) | \([]\) | \(40320\) | \(1.0296\) | \(\Gamma_0(N)\)-optimal |
35280.v2 | 35280eg2 | \([0, 0, 0, 132237, 9536562]\) | \(1747829720511/1280000000\) | \(-187280916480000000\) | \([]\) | \(282240\) | \(2.0026\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.v have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.v do not have complex multiplication.Modular form 35280.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.