Cremona's table of elliptic curves

40749 = 3 · 17² · 47

Field	Data	Notes
Atkin-Lehner	3+ 17+ 47+	Signs for the Atkin-Lehner involutions
Class	40749c	Isogeny class
Conductor	40749	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	60318720	Modular degree for the optimal curve
Δ	4.5639166755883E+29	Discriminant
Eigenvalues	0 3+ -3 -3  3  6 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3550653807,-74665957883650]	[a1,a2,a3,a4,a6]
Generators	[-1837996170636831985501765127970273332002546650315724:97316859343649747526112160458095244565655386252512350:46912020613477710915769746545457175360559189473]	Generators of the group modulo torsion
j	205095047944763221180383232/18907938390930371630541	j-invariant
L	3.1260868092083	L(r)(E,1)/r!
Ω	0.019673366914602	Real period
R	79.449715515853	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	122247o1 2397b1	Quadratic twists by: -3 17

Hecke Eigenvalues for elliptic curve 40749c1

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	+	-3	-3	3	6	+	6	5	1	-2	-3	10	0	+	8	-8	6	10	-12	-2	-11	-6	0	9

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Quadratic twists for elliptic curve 40749c1

-3	17
122247o1	2397b1

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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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