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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 93600.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.du1 | 93600bp1 | \([0, 0, 0, -2382825, -1413173500]\) | \(2052450196928704/4317958125\) | \(3147791473125000000\) | \([2]\) | \(1769472\) | \(2.4345\) | \(\Gamma_0(N)\)-optimal |
93600.du2 | 93600bp2 | \([0, 0, 0, -1562700, -2400604000]\) | \(-9045718037056/48125390625\) | \(-2245338225000000000000\) | \([2]\) | \(3538944\) | \(2.7811\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.du have rank \(1\).
Complex multiplication
The elliptic curves in class 93600.du do not have complex multiplication.Modular form 93600.2.a.du
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.