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	69696ew	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1106044742460506112 = 218 · 39 · 118	Discriminant
Eigenvalues	2- 3+ -4 -2 11- -2  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1163052,-480118320]	[a1,a2,a3,a4,a6]
Generators	[1276:10648:1]	Generators of the group modulo torsion
j	19034163/121	j-invariant
L	3.7911797329102	L(r)(E,1)/r!
Ω	0.14543404737991	Real period
R	3.2585042855418	Regulator
r	1	Rank of the group of rational points
S	0.9999999999212	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696s2 17424bh2 69696eu2 6336bu2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ew2

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

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Quadratic twists for elliptic curve 69696ew2

-4	8	-3	-11
69696s2	17424bh2	69696eu2	6336bu2

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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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