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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3366.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3366.p1 | 3366n2 | \([1, -1, 1, -11039, 260543]\) | \(204055591784617/78708537864\) | \(57378524102856\) | \([2]\) | \(10752\) | \(1.3391\) | |
| 3366.p2 | 3366n1 | \([1, -1, 1, -4919, -128689]\) | \(18052771191337/444958272\) | \(324374580288\) | \([2]\) | \(5376\) | \(0.99250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3366.p have rank \(0\).
Complex multiplication
The elliptic curves in class 3366.p do not have complex multiplication.Modular form 3366.2.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.
