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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 436800g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.g1 | 436800g1 | \([0, -1, 0, -2633, -7863]\) | \(31554496/17745\) | \(1135680000000\) | \([2]\) | \(737280\) | \(1.0033\) | \(\Gamma_0(N)\)-optimal |
436800.g2 | 436800g2 | \([0, -1, 0, 10367, -72863]\) | \(240641848/143325\) | \(-73382400000000\) | \([2]\) | \(1474560\) | \(1.3499\) |
Rank
sage: E.rank()
The elliptic curves in class 436800g have rank \(2\).
Complex multiplication
The elliptic curves in class 436800g do not have complex multiplication.Modular form 436800.2.a.g
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.