Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 6080.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6080.p1 | 6080p2 | \([0, 1, 0, -177921, 28826879]\) | \(-2376117230685121/342950\) | \(-89902284800\) | \([]\) | \(13824\) | \(1.5109\) | |
6080.p2 | 6080p1 | \([0, 1, 0, -1921, 49279]\) | \(-2992209121/2375000\) | \(-622592000000\) | \([]\) | \(4608\) | \(0.96155\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6080.p have rank \(1\).
Complex multiplication
The elliptic curves in class 6080.p do not have complex multiplication.Modular form 6080.2.a.p
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.