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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 4560.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.y1 | 4560i2 | \([0, 1, 0, -400, 2948]\) | \(6929294404/4275\) | \(4377600\) | \([2]\) | \(1536\) | \(0.21684\) | |
4560.y2 | 4560i1 | \([0, 1, 0, -20, 60]\) | \(-3631696/5415\) | \(-1386240\) | \([2]\) | \(768\) | \(-0.12974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.y have rank \(1\).
Complex multiplication
The elliptic curves in class 4560.y do not have complex multiplication.Modular form 4560.2.a.y
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.