Show commands:
SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 474320.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474320.cc1 | 474320cc2 | \([0, 1, 0, -46580200, 122352327348]\) | \(-5452947409/250\) | \(-512432265823937536000\) | \([]\) | \(40824000\) | \(3.0494\) | \(\Gamma_0(N)\)-optimal* |
474320.cc2 | 474320cc1 | \([0, 1, 0, -96840, 435770740]\) | \(-49/40\) | \(-81989162531830005760\) | \([]\) | \(13608000\) | \(2.5001\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474320.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 474320.cc do not have complex multiplication.Modular form 474320.2.a.cc
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.