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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 134640v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.ed1 | 134640v1 | \([0, 0, 0, -1224507, 521536106]\) | \(68001744211490809/1022422500\) | \(3052937226240000\) | \([2]\) | \(1548288\) | \(2.1078\) | \(\Gamma_0(N)\)-optimal |
134640.ed2 | 134640v2 | \([0, 0, 0, -1188507, 553640906]\) | \(-62178675647294809/8362782148050\) | \(-24971133689562931200\) | \([2]\) | \(3096576\) | \(2.4544\) |
Rank
sage: E.rank()
The elliptic curves in class 134640v have rank \(0\).
Complex multiplication
The elliptic curves in class 134640v do not have complex multiplication.Modular form 134640.2.a.v
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.