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	69696ex	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	439530729504768 = 224 · 39 · 113	Discriminant
Eigenvalues	2- 3-  0  0 11+  6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20460,-501424]	[a1,a2,a3,a4,a6]
Generators	[220:2376:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	6.2155572867419	L(r)(E,1)/r!
Ω	0.41739626553692	Real period
R	1.8614077916305	Regulator
r	1	Rank of the group of rational points
S	0.99999999996762	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696t1 17424bk1 23232cn1 69696ey1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ex1

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
-	-	0	0	+	6	-6	-6	6	-6	-4	2	6	-6	6	-12	12	6	4	-6	12	12	0	6	-10

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Quadratic twists for elliptic curve 69696ex1

-4	8	-3	-11
69696t1	17424bk1	23232cn1	69696ey1

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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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