Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 26640bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26640.y1 | 26640bw1 | \([0, 0, 0, -69132, -6995981]\) | \(3132662187311104/151723125\) | \(1769698530000\) | \([2]\) | \(86016\) | \(1.4228\) | \(\Gamma_0(N)\)-optimal |
26640.y2 | 26640bw2 | \([0, 0, 0, -65487, -7766534]\) | \(-166426126492624/43316015625\) | \(-8083808100000000\) | \([2]\) | \(172032\) | \(1.7694\) |
Rank
sage: E.rank()
The elliptic curves in class 26640bw have rank \(0\).
Complex multiplication
The elliptic curves in class 26640bw do not have complex multiplication.Modular form 26640.2.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.