Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 485520.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.r1 | 485520r2 | \([0, -1, 0, -7479416, -7870615200]\) | \(1872118575542884/17205615\) | \(425268960511933440\) | \([2]\) | \(14745600\) | \(2.5468\) | \(\Gamma_0(N)\)-optimal* |
485520.r2 | 485520r1 | \([0, -1, 0, -456716, -128790720]\) | \(-1705021456336/175670775\) | \(-1085507955928569600\) | \([2]\) | \(7372800\) | \(2.2002\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.r have rank \(1\).
Complex multiplication
The elliptic curves in class 485520.r do not have complex multiplication.Modular form 485520.2.a.r
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.