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SageMath
sage: E = EllipticCurve("e1")
sage: E.isogeny_class()
Elliptic curves in class 254320.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
254320.e1 | 254320e4 | [0, 1, 0, -2051996, 1130707480] | [2] | 4478976 | |
254320.e2 | 254320e3 | [0, 1, 0, -128701, 17504334] | [2] | 2239488 | |
254320.e3 | 254320e2 | [0, 1, 0, -28996, 1064280] | [2] | 1492992 | |
254320.e4 | 254320e1 | [0, 1, 0, -13101, -569726] | [2] | 746496 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254320.e have rank \(0\).
Complex multiplication
The elliptic curves in class 254320.e do not have complex multiplication.Modular form 254320.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.