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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 248256.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248256.f1 | 248256f2 | \([0, 0, 0, -41484, -24026096]\) | \(-41314084993/1281007856\) | \(-244804413560979456\) | \([]\) | \(2488320\) | \(2.0170\) | |
| 248256.f2 | 248256f1 | \([0, 0, 0, 4596, 875536]\) | \(56181887/1765376\) | \(-337368607358976\) | \([]\) | \(829440\) | \(1.4677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248256.f have rank \(1\).
Complex multiplication
The elliptic curves in class 248256.f do not have complex multiplication.Modular form 248256.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
