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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 93925.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93925.f1 | 93925j1 | \([1, 1, 1, -430038, 108353906]\) | \(23320116793/2873\) | \(1083550558390625\) | \([2]\) | \(884736\) | \(1.9083\) | \(\Gamma_0(N)\)-optimal |
93925.f2 | 93925j2 | \([1, 1, 1, -393913, 127355656]\) | \(-17923019113/8254129\) | \(-3113040754256265625\) | \([2]\) | \(1769472\) | \(2.2549\) |
Rank
sage: E.rank()
The elliptic curves in class 93925.f have rank \(0\).
Complex multiplication
The elliptic curves in class 93925.f do not have complex multiplication.Modular form 93925.2.a.f
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.