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SageMath
sage: E = EllipticCurve("p1")
sage: E.isogeny_class()
Elliptic curves in class 72450.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
72450.p1 | 72450u3 | [1, -1, 0, -649692, 66451216] | [2] | 1658880 | |
72450.p2 | 72450u1 | [1, -1, 0, -362817, -84023159] | [2] | 552960 | \(\Gamma_0(N)\)-optimal |
72450.p3 | 72450u2 | [1, -1, 0, -347067, -91661909] | [2] | 1105920 | |
72450.p4 | 72450u4 | [1, -1, 0, 2437308, 514066216] | [2] | 3317760 |
Rank
sage: E.rank()
The elliptic curves in class 72450.p have rank \(0\).
Complex multiplication
The elliptic curves in class 72450.p do not have complex multiplication.Modular form 72450.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.