Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 79350.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.br1 | 79350bu2 | \([1, 0, 1, -35284576, 51626426798]\) | \(84013940106985/28705554432\) | \(1659942292804300800000000\) | \([]\) | \(13685760\) | \(3.3494\) | |
79350.br2 | 79350bu1 | \([1, 0, 1, -14455201, -21151409452]\) | \(5776556465785/1073088\) | \(62052943771575000000\) | \([]\) | \(4561920\) | \(2.8001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79350.br have rank \(0\).
Complex multiplication
The elliptic curves in class 79350.br do not have complex multiplication.Modular form 79350.2.a.br
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 LMFDB 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 LMFDB labels.