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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 87120.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.cu1 | 87120eo2 | \([0, 0, 0, -103498923, 405276932698]\) | \(-23178622194826561/1610510\) | \(-8519360834577162240\) | \([]\) | \(8640000\) | \(3.0865\) | |
87120.cu2 | 87120eo1 | \([0, 0, 0, 173877, 112653178]\) | \(109902239/1100000\) | \(-5818838081126400000\) | \([]\) | \(1728000\) | \(2.2818\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.cu do not have complex multiplication.Modular form 87120.2.a.cu
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.