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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 16560.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.t1 | 16560bj2 | \([0, 0, 0, -456776283, -3710482422518]\) | \(3529773792266261468365081/50841342773437500000\) | \(151811436060000000000000000\) | \([2]\) | \(6635520\) | \(3.8278\) | |
16560.t2 | 16560bj1 | \([0, 0, 0, -3279963, -156975958262]\) | \(-1306902141891515161/3564268498800000000\) | \(-10642848709120819200000000\) | \([2]\) | \(3317760\) | \(3.4812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.t have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.t do not have complex multiplication.Modular form 16560.2.a.t
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.