Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 277725bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277725.bj1 | 277725bj1 | \([0, -1, 1, -282133, -178341207]\) | \(-1073741824/5325075\) | \(-12317222056510546875\) | \([]\) | \(5474304\) | \(2.3476\) | \(\Gamma_0(N)\)-optimal |
277725.bj2 | 277725bj2 | \([0, -1, 1, 2495117, 4366628418]\) | \(742692847616/3992296875\) | \(-9234425266289794921875\) | \([]\) | \(16422912\) | \(2.8969\) |
Rank
sage: E.rank()
The elliptic curves in class 277725bj have rank \(1\).
Complex multiplication
The elliptic curves in class 277725bj do not have complex multiplication.Modular form 277725.2.a.bj
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.