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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 51600.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.d1 | 51600bx2 | \([0, -1, 0, -66310408, 207857731312]\) | \(503835593418244309249/898614000000\) | \(57511296000000000000\) | \([2]\) | \(5806080\) | \(3.0499\) | |
| 51600.d2 | 51600bx1 | \([0, -1, 0, -4102408, 3317827312]\) | \(-119305480789133569/5200091136000\) | \(-332805832704000000000\) | \([2]\) | \(2903040\) | \(2.7033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.d have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.d do not have complex multiplication.Modular form 51600.2.a.d
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.
