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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 273600.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.m1 | 273600m1 | \([0, 0, 0, -5475, -155000]\) | \(24897088/171\) | \(124659000000\) | \([2]\) | \(458752\) | \(0.96286\) | \(\Gamma_0(N)\)-optimal |
| 273600.m2 | 273600m2 | \([0, 0, 0, -2100, -344000]\) | \(-21952/1083\) | \(-50528448000000\) | \([2]\) | \(917504\) | \(1.3094\) |
Rank
sage: E.rank()
The elliptic curves in class 273600.m have rank \(1\).
Complex multiplication
The elliptic curves in class 273600.m do not have complex multiplication.Modular form 273600.2.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.
