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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 436800o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.o2 | 436800o1 | \([0, -1, 0, 2040667, 600254037]\) | \(469904850632704/349938025983\) | \(-699876051966000000000\) | \([2]\) | \(20275200\) | \(2.6880\) | \(\Gamma_0(N)\)-optimal* |
436800.o1 | 436800o2 | \([0, -1, 0, -9366833, 5129031537]\) | \(2840220855817616/1288934561187\) | \(41245905957984000000000\) | \([2]\) | \(40550400\) | \(3.0346\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436800o have rank \(1\).
Complex multiplication
The elliptic curves in class 436800o do not have complex multiplication.Modular form 436800.2.a.o
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.