Cremona's table of elliptic curves

4697 = 7 · 11 · 61

Field	Data	Notes
Atkin-Lehner	7- 11- 61-	Signs for the Atkin-Lehner involutions
Class	4697c	Isogeny class
Conductor	4697	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	22061809 = 72 · 112 · 612	Discriminant
Eigenvalues	1  0 -2 7- 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-103,360]	[a1,a2,a3,a4,a6]
j	121508031177/22061809	j-invariant
L	1.0210218455427	L(r)(E,1)/r!
Ω	2.0420436910853	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	75152d2 42273d2 117425d2 32879c2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4697c2

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
1	0	-2	-	-	-2	-6	4	0	2	0	-2	-6	-4	4	-10	-4	-	4	0	10	8	12	6	2

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Quadratic twists for elliptic curve 4697c2

-4	-3	5	-7	-11
75152d2	42273d2	117425d2	32879c2	51667b2

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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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