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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 13860h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.v2 | 13860h1 | \([0, 0, 0, -852, -9571]\) | \(158328373248/21175\) | \(9147600\) | \([2]\) | \(5376\) | \(0.35488\) | \(\Gamma_0(N)\)-optimal |
| 13860.v1 | 13860h2 | \([0, 0, 0, -927, -7786]\) | \(12745567728/3587045\) | \(24793655040\) | \([2]\) | \(10752\) | \(0.70146\) |
Rank
sage: E.rank()
The elliptic curves in class 13860h have rank \(1\).
Complex multiplication
The elliptic curves in class 13860h do not have complex multiplication.Modular form 13860.2.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.
