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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 9576e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.p2 | 9576e1 | \([0, 0, 0, -75, 54]\) | \(1687500/931\) | \(25740288\) | \([2]\) | \(1536\) | \(0.11252\) | \(\Gamma_0(N)\)-optimal |
| 9576.p1 | 9576e2 | \([0, 0, 0, -915, 10638]\) | \(1532121750/2527\) | \(139732992\) | \([2]\) | \(3072\) | \(0.45909\) |
Rank
sage: E.rank()
The elliptic curves in class 9576e have rank \(1\).
Complex multiplication
The elliptic curves in class 9576e do not have complex multiplication.Modular form 9576.2.a.e
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.
