Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 485520n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.n2 | 485520n1 | \([0, -1, 0, -2439256, -157205354000]\) | \(-16234636151161/107977095878400\) | \(-10675423650547694016921600\) | \([2]\) | \(88473600\) | \(3.4814\) | \(\Gamma_0(N)\)-optimal* |
485520.n1 | 485520n2 | \([0, -1, 0, -451892056, -3647835579920]\) | \(103222496159832099961/1586991144921840\) | \(156901819445001882038108160\) | \([2]\) | \(176947200\) | \(3.8280\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520n have rank \(0\).
Complex multiplication
The elliptic curves in class 485520n do not have complex multiplication.Modular form 485520.2.a.n
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 Cremona 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 Cremona labels.