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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 45980c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45980.e1 | 45980c1 | \([0, -1, 0, -111481, -13324650]\) | \(5405726654464/407253125\) | \(11543580054050000\) | \([2]\) | \(345600\) | \(1.8273\) | \(\Gamma_0(N)\)-optimal |
45980.e2 | 45980c2 | \([0, -1, 0, 106924, -59364424]\) | \(298091207216/3525390625\) | \(-1598833802500000000\) | \([2]\) | \(691200\) | \(2.1739\) |
Rank
sage: E.rank()
The elliptic curves in class 45980c have rank \(0\).
Complex multiplication
The elliptic curves in class 45980c do not have complex multiplication.Modular form 45980.2.a.c
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.