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	69696dl	Isogeny class
Conductor	69696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	-909193450176 = -1 · 26 · 36 · 117	Discriminant
Eigenvalues	2+ 3- -3 -4 11- -2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,726,-45254]	[a1,a2,a3,a4,a6]
Generators	[33:121:1]	Generators of the group modulo torsion
j	512/11	j-invariant
L	1.8999474397571	L(r)(E,1)/r!
Ω	0.42968395020506	Real period
R	1.1054330976073	Regulator
r	1	Rank of the group of rational points
S	0.99999999973043	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696dk1 34848bc1 7744g1 6336t1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dl1

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
+	-	-3	-4	-	-2	-8	-6	5	-4	-1	-3	-6	6	-12	-6	-3	0	11	-5	10	-2	-2	5	13

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Quadratic twists for elliptic curve 69696dl1

-4	8	-3	-11
69696dk1	34848bc1	7744g1	6336t1

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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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