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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 73926.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73926.n1 | 73926y3 | \([1, -1, 1, -168644, -35302553]\) | \(-1167051/512\) | \(-232709496921662976\) | \([]\) | \(933120\) | \(2.0396\) | |
73926.n2 | 73926y1 | \([1, -1, 1, -4364, 113477]\) | \(-132651/2\) | \(-138549226086\) | \([]\) | \(103680\) | \(0.94095\) | \(\Gamma_0(N)\)-optimal |
73926.n3 | 73926y2 | \([1, -1, 1, 16171, 551557]\) | \(9261/8\) | \(-404009543266776\) | \([]\) | \(311040\) | \(1.4903\) |
Rank
sage: E.rank()
The elliptic curves in class 73926.n have rank \(1\).
Complex multiplication
The elliptic curves in class 73926.n do not have complex multiplication.Modular form 73926.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.