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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 96600.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.w1 | 96600bx2 | \([0, -1, 0, -2528, -27348]\) | \(6982110826/2699487\) | \(691068672000\) | \([2]\) | \(153600\) | \(0.97075\) | |
| 96600.w2 | 96600bx1 | \([0, -1, 0, -1128, 14652]\) | \(1241154932/30429\) | \(3894912000\) | \([2]\) | \(76800\) | \(0.62418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.w have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.w do not have complex multiplication.Modular form 96600.2.a.w
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.
