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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 77616.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.h1 | 77616fv2 | \([0, 0, 0, -52532067, -146512439710]\) | \(45637459887836881/13417633152\) | \(4713588115243185733632\) | \([2]\) | \(12386304\) | \(3.1377\) | |
| 77616.h2 | 77616fv1 | \([0, 0, 0, -2857827, -2904211870]\) | \(-7347774183121/6119866368\) | \(-2149897008831359090688\) | \([2]\) | \(6193152\) | \(2.7912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.h have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.h do not have complex multiplication.Modular form 77616.2.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.
