Cremona's table of elliptic curves

6996 = 2² · 3 · 11 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 53-	Signs for the Atkin-Lehner involutions
Class	6996a	Isogeny class
Conductor	6996	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	4925184 = 28 · 3 · 112 · 53	Discriminant
Eigenvalues	2- 3- -2  2 11- -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-844,-9724]	[a1,a2,a3,a4,a6]
Generators	[64:450:1]	Generators of the group modulo torsion
j	260031254992/19239	j-invariant
L	4.6120531330759	L(r)(E,1)/r!
Ω	0.8856721713172	Real period
R	3.4716029116557	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27984d2 111936b2 20988b2 76956c2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6996a2

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
-	-	-2	2	-	-2	0	-4	-4	8	8	-10	-2	-2	-8	-	4	-8	12	0	8	-12	-10	2	-2

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Quadratic twists for elliptic curve 6996a2

-4	8	-3	-11
27984d2	111936b2	20988b2	76956c2

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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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