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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 476850.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.p1 | 476850p2 | \([1, 1, 0, -82820325, -320535637875]\) | \(-6663170841705625/850403524608\) | \(-8018231934792499200000000\) | \([]\) | \(123171840\) | \(3.5124\) | |
476850.p2 | 476850p1 | \([1, 1, 0, 6589050, 998356500]\) | \(3355354844375/1987172352\) | \(-18736527250504800000000\) | \([]\) | \(41057280\) | \(2.9631\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850.p have rank \(0\).
Complex multiplication
The elliptic curves in class 476850.p do not have complex multiplication.Modular form 476850.2.a.p
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.