Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 58800.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.by1 | 58800gm2 | \([0, -1, 0, -4469208, 3638076912]\) | \(2569823930905/72\) | \(276595200000000\) | \([]\) | \(933120\) | \(2.2818\) | |
58800.by2 | 58800gm1 | \([0, -1, 0, -59208, 4236912]\) | \(5975305/1458\) | \(5601052800000000\) | \([]\) | \(311040\) | \(1.7325\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.by have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.by do not have complex multiplication.Modular form 58800.2.a.by
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.