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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 215600fy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.m2 | 215600fy1 | \([0, 1, 0, 14292, -1027412]\) | \(5488/11\) | \(-647069500000000\) | \([2]\) | \(921600\) | \(1.5264\) | \(\Gamma_0(N)\)-optimal |
| 215600.m1 | 215600fy2 | \([0, 1, 0, -108208, -11072412]\) | \(595508/121\) | \(28471058000000000\) | \([2]\) | \(1843200\) | \(1.8730\) |
Rank
sage: E.rank()
The elliptic curves in class 215600fy have rank \(1\).
Complex multiplication
The elliptic curves in class 215600fy do not have complex multiplication.Modular form 215600.2.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 Cremona 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 Cremona labels.
