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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 148800.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148800.br1 | 148800kf2 | \([0, -1, 0, -59908033, 166512447937]\) | \(5805223604235668521/435937500000000\) | \(1785600000000000000000000\) | \([2]\) | \(24772608\) | \(3.3988\) | |
148800.br2 | 148800kf1 | \([0, -1, 0, 3579967, 11538239937]\) | \(1238798620042199/14760960000000\) | \(-60460892160000000000000\) | \([2]\) | \(12386304\) | \(3.0523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148800.br have rank \(0\).
Complex multiplication
The elliptic curves in class 148800.br do not have complex multiplication.Modular form 148800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.