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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 862.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 862.d1 | 862e1 | \([1, 1, 1, -2460, 45949]\) | \(-1646417855125441/451936256\) | \(-451936256\) | \([5]\) | \(640\) | \(0.64323\) | \(\Gamma_0(N)\)-optimal |
| 862.d2 | 862e2 | \([1, 1, 1, 15380, -102531]\) | \(402337908227545919/237961300338416\) | \(-237961300338416\) | \([]\) | \(3200\) | \(1.4479\) |
Rank
sage: E.rank()
The elliptic curves in class 862.d have rank \(1\).
Complex multiplication
The elliptic curves in class 862.d do not have complex multiplication.Modular form 862.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
