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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 90160bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90160.l2 | 90160bw1 | \([0, 1, 0, -7150096, 7050179604]\) | \(83890194895342081/3958384640000\) | \(1907507177518530560000\) | \([2]\) | \(5160960\) | \(2.8441\) | \(\Gamma_0(N)\)-optimal |
| 90160.l1 | 90160bw2 | \([0, 1, 0, -19694096, -24465365996]\) | \(1753007192038126081/478174101507200\) | \(230427463140231466188800\) | \([2]\) | \(10321920\) | \(3.1906\) |
Rank
sage: E.rank()
The elliptic curves in class 90160bw have rank \(1\).
Complex multiplication
The elliptic curves in class 90160bw do not have complex multiplication.Modular form 90160.2.a.bw
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.
