Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 84042bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84042.bq2 | 84042bw1 | \([1, -1, 1, -97230254, -370974886995]\) | \(-139444195316122186685933977/867810592237096964848\) | \(-632633921740843687374192\) | \([2]\) | \(17461248\) | \(3.4053\) | \(\Gamma_0(N)\)-optimal |
84042.bq1 | 84042bw2 | \([1, -1, 1, -1558000274, -23669672397987]\) | \(573718392227901342193352375257/22016176259779893044\) | \(16049792493379542029076\) | \([2]\) | \(34922496\) | \(3.7518\) |
Rank
sage: E.rank()
The elliptic curves in class 84042bw have rank \(0\).
Complex multiplication
The elliptic curves in class 84042bw do not have complex multiplication.Modular form 84042.2.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.