Cremona's table of elliptic curves

69696 = 2⁶ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	69696dr	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-46085197602521088 = -1 · 215 · 38 · 118	Discriminant
Eigenvalues	2+ 3- -4 -2 11-  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1452,10328560]	[a1,a2,a3,a4,a6]
Generators	[77:3267:1]	Generators of the group modulo torsion
j	-8/1089	j-invariant
L	4.1648379410271	L(r)(E,1)/r!
Ω	0.28594331130703	Real period
R	1.8206571795008	Regulator
r	1	Rank of the group of rational points
S	0.99999999993665	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696dp2 34848ck2 23232ck2 6336bf2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dr2

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
+	-	-4	-2	-	4	2	-4	6	6	-4	2	6	-8	10	-12	0	8	4	6	-10	-6	-12	14	-18

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Quadratic twists for elliptic curve 69696dr2

-4	8	-3	-11
69696dp2	34848ck2	23232ck2	6336bf2

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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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