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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 96774h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96774.h2 | 96774h1 | \([1, 1, 1, -1644287370, -25421911900521]\) | \(117174888570509216929/1273887851544576\) | \(5345071532647248231728676864\) | \([]\) | \(59609088\) | \(4.1356\) | \(\Gamma_0(N)\)-optimal |
96774.h1 | 96774h2 | \([1, 1, 1, -360662279010, 83367811912911159]\) | \(1236526859255318155975783969/38367061931916216\) | \(160983315976322668502863696824\) | \([]\) | \(417263616\) | \(5.1086\) |
Rank
sage: E.rank()
The elliptic curves in class 96774h have rank \(1\).
Complex multiplication
The elliptic curves in class 96774h do not have complex multiplication.Modular form 96774.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.