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	69696b	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	6083246083532783616 = 217 · 39 · 119	Discriminant
Eigenvalues	2+ 3+  2 -2 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6181164,-5913792720]	[a1,a2,a3,a4,a6]
Generators	[-123066819603:93536352575:85766121]	Generators of the group modulo torsion
j	4293378	j-invariant
L	6.937656892681	L(r)(E,1)/r!
Ω	0.09574984028255	Real period
R	18.114016881646	Regulator
r	1	Rank of the group of rational points
S	0.9999999999292	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696du2 8712p2 69696d2 69696a2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696b2

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
+	+	2	-2	+	2	-2	4	-6	-2	0	2	6	-8	-2	10	-4	14	4	-6	-8	2	12	8	-2

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Quadratic twists for elliptic curve 69696b2

-4	8	-3	-11
69696du2	8712p2	69696d2	69696a2

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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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