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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 73926.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73926.j1 | 73926c3 | \([1, -1, 0, -39273, -3024613]\) | \(-132651/2\) | \(-101002385816694\) | \([]\) | \(311040\) | \(1.4903\) | |
73926.j2 | 73926c2 | \([1, -1, 0, -18738, 1313748]\) | \(-1167051/512\) | \(-319217416902144\) | \([]\) | \(311040\) | \(1.4903\) | |
73926.j3 | 73926c1 | \([1, -1, 0, 1797, -21027]\) | \(9261/8\) | \(-554196904344\) | \([]\) | \(103680\) | \(0.94095\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73926.j have rank \(1\).
Complex multiplication
The elliptic curves in class 73926.j do not have complex multiplication.Modular form 73926.2.a.j
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.