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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 147294.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.x1 | 147294cm2 | \([1, -1, 0, -799983, -305754107]\) | \(-274952937217/37259704\) | \(-7672684296333329784\) | \([]\) | \(3846528\) | \(2.3559\) | |
147294.x2 | 147294cm1 | \([1, -1, 0, 64377, 1093693]\) | \(143286143/85504\) | \(-17607364730371584\) | \([]\) | \(1282176\) | \(1.8066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147294.x have rank \(1\).
Complex multiplication
The elliptic curves in class 147294.x do not have complex multiplication.Modular form 147294.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.