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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 67600dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.o2 | 67600dm1 | \([0, 1, 0, -62248, 4792308]\) | \(4913\) | \(5429503678976000\) | \([2]\) | \(319488\) | \(1.7349\) | \(\Gamma_0(N)\)-optimal |
67600.o1 | 67600dm2 | \([0, 1, 0, -941048, 351039508]\) | \(16974593\) | \(5429503678976000\) | \([2]\) | \(638976\) | \(2.0814\) |
Rank
sage: E.rank()
The elliptic curves in class 67600dm have rank \(0\).
Complex multiplication
The elliptic curves in class 67600dm do not have complex multiplication.Modular form 67600.2.a.dm
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.