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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 423864.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
423864.bj1 | 423864bj2 | \([0, 0, 0, -270730515, -1714505580146]\) | \(2471097448795250/98942809\) | \(87867790098081985087488\) | \([2]\) | \(61931520\) | \(3.4854\) | \(\Gamma_0(N)\)-optimal* |
423864.bj2 | 423864bj1 | \([0, 0, 0, -16109355, -29473667498]\) | \(-1041220466500/242597383\) | \(-107721299522575728073728\) | \([2]\) | \(30965760\) | \(3.1389\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 423864.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 423864.bj do not have complex multiplication.Modular form 423864.2.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 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.