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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 9576c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.o2 | 9576c1 | \([0, 0, 0, 270, -3159]\) | \(6912000/17689\) | \(-5570761392\) | \([2]\) | \(4608\) | \(0.55383\) | \(\Gamma_0(N)\)-optimal |
| 9576.o1 | 9576c2 | \([0, 0, 0, -2295, -35478]\) | \(265302000/45619\) | \(229867206912\) | \([2]\) | \(9216\) | \(0.90040\) |
Rank
sage: E.rank()
The elliptic curves in class 9576c have rank \(0\).
Complex multiplication
The elliptic curves in class 9576c do not have complex multiplication.Modular form 9576.2.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.
