Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 115920.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.co1 | 115920ee1 | \([0, 0, 0, -543587547, -4875769801334]\) | \(5949010462538271898545049/3314625947988102720\) | \(9897420046677306912276480\) | \([2]\) | \(40734720\) | \(3.7436\) | \(\Gamma_0(N)\)-optimal |
115920.co2 | 115920ee2 | \([0, 0, 0, -446779227, -6667362656246]\) | \(-3303050039017428591035929/4519896503737558217400\) | \(-13496338641816289036224921600\) | \([2]\) | \(81469440\) | \(4.0902\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.co have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.co do not have complex multiplication.Modular form 115920.2.a.co
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.