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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 82524.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82524.f1 | 82524e2 | \([0, -1, 0, -10756, 377608]\) | \(3631696/507\) | \(19213874105088\) | \([2]\) | \(304128\) | \(1.2752\) | |
| 82524.f2 | 82524e1 | \([0, -1, 0, -2821, -50882]\) | \(1048576/117\) | \(277123184208\) | \([2]\) | \(152064\) | \(0.92865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82524.f have rank \(0\).
Complex multiplication
The elliptic curves in class 82524.f do not have complex multiplication.Modular form 82524.2.a.f
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.
