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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2475.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2475.c1 | 2475d2 | \([1, -1, 1, -3755, -87128]\) | \(19034163/121\) | \(37213171875\) | \([2]\) | \(1920\) | \(0.86533\) | |
2475.c2 | 2475d1 | \([1, -1, 1, -380, 622]\) | \(19683/11\) | \(3383015625\) | \([2]\) | \(960\) | \(0.51876\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2475.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2475.c do not have complex multiplication.Modular form 2475.2.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 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.