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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 139650.fy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139650.fy1 | 139650ek1 | \([1, 1, 1, -493438, 133207031]\) | \(2479176213198607/541500\) | \(2902101562500\) | \([2]\) | \(1105920\) | \(1.7751\) | \(\Gamma_0(N)\)-optimal |
| 139650.fy2 | 139650ek2 | \([1, 1, 1, -491688, 134201031]\) | \(-2452892123873647/36652781250\) | \(-196435999511718750\) | \([2]\) | \(2211840\) | \(2.1217\) |
Rank
sage: E.rank()
The elliptic curves in class 139650.fy have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.fy do not have complex multiplication.Modular form 139650.2.a.fy
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.
