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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 85176.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85176.y1 | 85176m2 | \([0, 0, 0, -253076655, -1549622431838]\) | \(1989996724085074000/1843096437\) | \(1660258326685460366592\) | \([2]\) | \(10321920\) | \(3.3687\) | |
85176.y2 | 85176m1 | \([0, 0, 0, -15701790, -24583874159]\) | \(-7604375980288000/236743082667\) | \(-13328611921510615849392\) | \([2]\) | \(5160960\) | \(3.0221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.y have rank \(0\).
Complex multiplication
The elliptic curves in class 85176.y do not have complex multiplication.Modular form 85176.2.a.y
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.