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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 46893n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46893.p3 | 46893n1 | \([1, 0, 1, -2427, -45671]\) | \(13430356633/180873\) | \(21279527577\) | \([2]\) | \(39936\) | \(0.78841\) | \(\Gamma_0(N)\)-optimal |
46893.p2 | 46893n2 | \([1, 0, 1, -4632, 49585]\) | \(93391282153/44876601\) | \(5279687231049\) | \([2, 2]\) | \(79872\) | \(1.1350\) | |
46893.p4 | 46893n3 | \([1, 0, 1, 16683, 382099]\) | \(4365111505607/3058314567\) | \(-359807650492983\) | \([2]\) | \(159744\) | \(1.4816\) | |
46893.p1 | 46893n4 | \([1, 0, 1, -61227, 5822275]\) | \(215751695207833/163381911\) | \(19221718447239\) | \([2]\) | \(159744\) | \(1.4816\) |
Rank
sage: E.rank()
The elliptic curves in class 46893n have rank \(0\).
Complex multiplication
The elliptic curves in class 46893n do not have complex multiplication.Modular form 46893.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.