Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 26928bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.bu2 | 26928bw1 | \([0, 0, 0, -78699, 8314778]\) | \(18052771191337/444958272\) | \(1328638280859648\) | \([2]\) | \(129024\) | \(1.6856\) | \(\Gamma_0(N)\)-optimal |
26928.bu1 | 26928bw2 | \([0, 0, 0, -176619, -16498150]\) | \(204055591784617/78708537864\) | \(235022434725298176\) | \([2]\) | \(258048\) | \(2.0322\) |
Rank
sage: E.rank()
The elliptic curves in class 26928bw have rank \(1\).
Complex multiplication
The elliptic curves in class 26928bw do not have complex multiplication.Modular form 26928.2.a.bw
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.