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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 96600.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.y1 | 96600w2 | \([0, -1, 0, -4929128, 4209481452]\) | \(51736151918874580666/61189598466927\) | \(15664537207533312000\) | \([2]\) | \(3532800\) | \(2.5947\) | |
| 96600.y2 | 96600w1 | \([0, -1, 0, -4927728, 4211993052]\) | \(103384162441255867412/144872469\) | \(18543676032000\) | \([2]\) | \(1766400\) | \(2.2481\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.y have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.y do not have complex multiplication.Modular form 96600.2.a.y
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.
