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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 91035.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.bo1 | 91035be2 | \([1, -1, 0, -546264, 76054545]\) | \(208527857/91875\) | \(7942645380655006875\) | \([2]\) | \(1671168\) | \(2.3224\) | |
| 91035.bo2 | 91035be1 | \([1, -1, 0, 116991, 8800488]\) | \(2048383/1575\) | \(-136159635096942975\) | \([2]\) | \(835584\) | \(1.9758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.bo do not have complex multiplication.Modular form 91035.2.a.bo
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.
