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
deg	737280	Modular degree for the optimal curve
Δ	100549522041864192 = 218 · 39 · 117	Discriminant
Eigenvalues	2- 3+ -4 -2 11- -2  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-117612,2874960]	[a1,a2,a3,a4,a6]
Generators	[682:15488:1]	Generators of the group modulo torsion
j	19683/11	j-invariant
L	3.7911797329102	L(r)(E,1)/r!
Ω	0.29086809475982	Real period
R	1.6292521427709	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	69696s1 17424bh1 69696eu1 6336bu1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ew1

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 69696ew1

-4	8	-3	-11
69696s1	17424bh1	69696eu1	6336bu1

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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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