Cremona's table of elliptic curves

6293 = 7 · 29 · 31

Field	Data	Notes
Atkin-Lehner	7+ 29+ 31+	Signs for the Atkin-Lehner involutions
Class	6293a	Isogeny class
Conductor	6293	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-9559067 = -1 · 73 · 29 · 312	Discriminant
Eigenvalues	0 -1  0 7+ -2  4 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-33,177]	[a1,a2,a3,a4,a6]
Generators	[-3:15:1]	Generators of the group modulo torsion
j	-4096000000/9559067	j-invariant
L	2.3293591880865	L(r)(E,1)/r!
Ω	2.0390038441507	Real period
R	0.57120029341012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	100688ba1 56637e1 44051e1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6293a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	-1	0	+	-2	4	-2	-5	7	+	+	0	7	8	3	-5	-4	6	-5	7	11	6	-12	-9	9

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Quadratic twists for elliptic curve 6293a1

-4	-3	-7
100688ba1	56637e1	44051e1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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