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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 49725m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.h1 | 49725m1 | \([1, -1, 1, -4505, 106872]\) | \(887503681/89505\) | \(1019517890625\) | \([2]\) | \(61440\) | \(1.0403\) | \(\Gamma_0(N)\)-optimal |
49725.h2 | 49725m2 | \([1, -1, 1, 5620, 511872]\) | \(1723683599/10989225\) | \(-125174141015625\) | \([2]\) | \(122880\) | \(1.3869\) |
Rank
sage: E.rank()
The elliptic curves in class 49725m have rank \(1\).
Complex multiplication
The elliptic curves in class 49725m do not have complex multiplication.Modular form 49725.2.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 Cremona 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 Cremona labels.