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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 289800.ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
289800.ea1 | 289800ea2 | \([0, 0, 0, -220275, -39791250]\) | \(50668941906/1127\) | \(26290656000000\) | \([2]\) | \(1048576\) | \(1.6900\) | |
289800.ea2 | 289800ea1 | \([0, 0, 0, -13275, -668250]\) | \(-22180932/3703\) | \(-43191792000000\) | \([2]\) | \(524288\) | \(1.3434\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 289800.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 289800.ea do not have complex multiplication.Modular form 289800.2.a.ea
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.