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	69696et	Isogeny class
Conductor	69696	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-195920474112 = -1 · 212 · 33 · 116	Discriminant
Eigenvalues	2- 3+  4  0 11- -6  8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1452,0]	[a1,a2,a3,a4,a6]
Generators	[204490:2974543:1000]	Generators of the group modulo torsion
j	1728	j-invariant
L	9.1525252001107	L(r)(E,1)/r!
Ω	0.60071097139993	Real period
R	7.6180772753705	Regulator
r	1	Rank of the group of rational points
S	0.99999999994926	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696et2 34848bo1 69696ev2 576f2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696et2

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	0	-	-6	8	0	0	4	0	2	-8	0	0	-4	0	-10	0	0	-6	0	0	-16	-18

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Quadratic twists for elliptic curve 69696et2

-4	8	-3	-11
69696et2	34848bo1	69696ev2	576f2

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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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