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	69696ds	Isogeny class
Conductor	69696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-4335648768 = -1 · 214 · 37 · 112	Discriminant
Eigenvalues	2+ 3- -4  5 11- -2  4  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7392,244640]	[a1,a2,a3,a4,a6]
Generators	[49:9:1]	Generators of the group modulo torsion
j	-30908416/3	j-invariant
L	5.7391033333763	L(r)(E,1)/r!
Ω	1.3232605989236	Real period
R	1.084273071168	Regulator
r	1	Rank of the group of rational points
S	0.99999999985611	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696he1 4356k1 23232bc1 69696dt1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ds1

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	5	-	-2	4	3	-6	2	1	-7	-10	4	2	-2	-6	7	-9	-8	3	-1	14	-4	13

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Quadratic twists for elliptic curve 69696ds1

-4	8	-3	-11
69696he1	4356k1	23232bc1	69696dt1

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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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