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	69696bp	Isogeny class
Conductor	69696	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-909193450176 = -1 · 26 · 36 · 117	Discriminant
Eigenvalues	2+ 3-  1  2 11-  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-34065372,-76527551342]	[a1,a2,a3,a4,a6]
Generators	[147525391266941406826761203799270781906686460086712472138102712299104743078518926095:41004334004905324812443009795422091682746902313289075742955176247403255520076445350713:1898508269354665163441491510953995594071773231676986406218813120707046288045125]	Generators of the group modulo torsion
j	-52893159101157376/11	j-invariant
L	8.0655993339613	L(r)(E,1)/r!
Ω	0.031245773125722	Real period
R	129.06704694917	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696fw3 1089j3 7744f3 6336y3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696bp3

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	2	-	4	-2	0	1	0	7	-3	-8	-6	-8	-6	5	12	7	3	-4	10	6	-15	-7

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Quadratic twists for elliptic curve 69696bp3

-4	8	-3	-11
69696fw3	1089j3	7744f3	6336y3

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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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