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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 311696h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.h2 | 311696h1 | \([0, 1, 0, -448708, 115785756]\) | \(-22030281250000/54215623\) | \(-24587848524160768\) | \([2]\) | \(2580480\) | \(2.0233\) | \(\Gamma_0(N)\)-optimal |
311696.h1 | 311696h2 | \([0, 1, 0, -7183568, 7408292164]\) | \(22598953394030500/136367\) | \(247380437900288\) | \([2]\) | \(5160960\) | \(2.3699\) |
Rank
sage: E.rank()
The elliptic curves in class 311696h have rank \(0\).
Complex multiplication
The elliptic curves in class 311696h do not have complex multiplication.Modular form 311696.2.a.h
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.