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	69696a	Isogeny class
Conductor	69696	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3433833824256 = 217 · 39 · 113	Discriminant
Eigenvalues	2+ 3+  2  2 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-51084,4443120]	[a1,a2,a3,a4,a6]
Generators	[388:6560:1]	Generators of the group modulo torsion
j	4293378	j-invariant
L	7.9343981193243	L(r)(E,1)/r!
Ω	0.77190194918789	Real period
R	5.13951164912	Regulator
r	1	Rank of the group of rational points
S	0.99999999995778	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696dv2 8712b2 69696c2 69696b2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696a2

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 69696a2

-4	8	-3	-11
69696dv2	8712b2	69696c2	69696b2

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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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