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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 481338.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.m1 | 481338m2 | \([1, -1, 0, -407028, 100052200]\) | \(207517798057524921/66033032\) | \(2373029070984\) | \([2]\) | \(3096576\) | \(1.7355\) | \(\Gamma_0(N)\)-optimal* |
481338.m2 | 481338m1 | \([1, -1, 0, -25548, 1554064]\) | \(51317108404281/903363136\) | \(32464161018432\) | \([2]\) | \(1548288\) | \(1.3889\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 481338.m have rank \(2\).
Complex multiplication
The elliptic curves in class 481338.m do not have complex multiplication.Modular form 481338.2.a.m
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.