Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 422331be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.be2 | 422331be1 | \([0, -1, 1, 5521, 758708]\) | \(32768/459\) | \(-260651986686819\) | \([]\) | \(1347840\) | \(1.4469\) | \(\Gamma_0(N)\)-optimal* |
422331.be1 | 422331be2 | \([0, -1, 1, -491339, 132799253]\) | \(-23100424192/14739\) | \(-8369824905832299\) | \([]\) | \(4043520\) | \(1.9962\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422331be have rank \(1\).
Complex multiplication
The elliptic curves in class 422331be do not have complex multiplication.Modular form 422331.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.