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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 95139.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95139.h1 | 95139e2 | \([1, -1, 0, -1245636, 487901637]\) | \(11089567/1089\) | \(20989913680535654151\) | \([2]\) | \(1777664\) | \(2.4445\) | |
95139.h2 | 95139e1 | \([1, -1, 0, 94959, 36657360]\) | \(4913/33\) | \(-636057990319262247\) | \([2]\) | \(888832\) | \(2.0979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95139.h have rank \(1\).
Complex multiplication
The elliptic curves in class 95139.h do not have complex multiplication.Modular form 95139.2.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 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.