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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 2496.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.p1 | 2496p1 | \([0, 1, 0, -2605, 47219]\) | \(1909913257984/129730653\) | \(132844188672\) | \([2]\) | \(3840\) | \(0.88296\) | \(\Gamma_0(N)\)-optimal |
| 2496.p2 | 2496p2 | \([0, 1, 0, 2255, 207599]\) | \(77366117936/1172914587\) | \(-19217032593408\) | \([2]\) | \(7680\) | \(1.2295\) |
Rank
sage: E.rank()
The elliptic curves in class 2496.p have rank \(1\).
Complex multiplication
The elliptic curves in class 2496.p do not have complex multiplication.Modular form 2496.2.a.p
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.
