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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 145794.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145794.s1 | 145794x2 | \([1, 0, 1, -652613541476, 202980780076995170]\) | \(-2851706381404169233907849265625/933517927940580307894272\) | \(-10062590758753420656009476453695488\) | \([]\) | \(1945866240\) | \(5.4982\) | |
145794.s2 | 145794x1 | \([1, 0, 1, 4459903579, 1036296713675792]\) | \(910149999888914847380375/43565940803046185238528\) | \(-469606656926502009818114538995712\) | \([]\) | \(648622080\) | \(4.9489\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145794.s have rank \(0\).
Complex multiplication
The elliptic curves in class 145794.s do not have complex multiplication.Modular form 145794.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.