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	69696fi	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	4055040	Modular degree for the optimal curve
Δ	2.7374607375898E+19	Discriminant
Eigenvalues	2- 3- -4  4 11+ -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4008972,3079295120]	[a1,a2,a3,a4,a6]
Generators	[1258:5184:1]	Generators of the group modulo torsion
j	63253004/243	j-invariant
L	3.9849330918791	L(r)(E,1)/r!
Ω	0.21174551111491	Real period
R	2.3524306785261	Regulator
r	1	Rank of the group of rational points
S	1.0000000001967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696bh1 17424m1 23232cr1 69696fj1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696fi1

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

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Quadratic twists for elliptic curve 69696fi1

-4	8	-3	-11
69696bh1	17424m1	23232cr1	69696fj1

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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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