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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 364650.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.m1 | 364650m2 | \([1, 1, 0, -18980, -1014000]\) | \(6049759017137597/2785109184\) | \(348138648000\) | \([2]\) | \(884736\) | \(1.1714\) | |
364650.m2 | 364650m1 | \([1, 1, 0, -1380, -10800]\) | \(2327783545277/985780224\) | \(123222528000\) | \([2]\) | \(442368\) | \(0.82485\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.m have rank \(2\).
Complex multiplication
The elliptic curves in class 364650.m do not have complex multiplication.Modular form 364650.2.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.