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	69696dq	Isogeny class
Conductor	69696	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	3686400	Modular degree for the optimal curve
Δ	9.2666439513782E+20	Discriminant
Eigenvalues	2+ 3- -4  2 11-  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3137772,1559399600]	[a1,a2,a3,a4,a6]
Generators	[-275:49005:1]	Generators of the group modulo torsion
j	10091699281/2737152	j-invariant
L	5.0266133862517	L(r)(E,1)/r!
Ω	0.1466776443268	Real period
R	2.1418624362444	Regulator
r	1	Rank of the group of rational points
S	1.0000000000647	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696hc1 2178m1 23232ba1 6336bg1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dq1

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

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Quadratic twists for elliptic curve 69696dq1

-4	8	-3	-11
69696hc1	2178m1	23232ba1	6336bg1

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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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