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	69696bq	Isogeny class
Conductor	69696	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-2797938671616 = -1 · 218 · 36 · 114	Discriminant
Eigenvalues	2+ 3-  1 -2 11- -1  5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1452,83248]	[a1,a2,a3,a4,a6]
Generators	[38:288:1]	Generators of the group modulo torsion
j	-121	j-invariant
L	6.1381611117877	L(r)(E,1)/r!
Ω	0.69040438516457	Real period
R	1.1113343938557	Regulator
r	1	Rank of the group of rational points
S	1.0000000000929	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696fs1 1089h1 7744m1 69696bo2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696bq1

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
+	-	1	-2	-	-1	5	-6	-2	9	-2	3	5	0	-2	9	8	-6	-2	-12	-2	-10	6	9	-13

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Quadratic twists for elliptic curve 69696bq1

-4	8	-3	-11
69696fs1	1089h1	7744m1	69696bo2

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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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