Cremona's table of elliptic curves

7686 = 2 · 3² · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 61-	Signs for the Atkin-Lehner involutions
Class	7686x	Isogeny class
Conductor	7686	Conductor
∏ cp	168	Product of Tamagawa factors cp
deg	24192	Modular degree for the optimal curve
Δ	-28021207568256 = -1 · 27 · 39 · 72 · 613	Discriminant
Eigenvalues	2- 3- -3 7-  0 -4 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11804,-552481]	[a1,a2,a3,a4,a6]
Generators	[519:-11789:1]	Generators of the group modulo torsion
j	-249487788397177/38437870464	j-invariant
L	5.256260984402	L(r)(E,1)/r!
Ω	0.22708739257796	Real period
R	0.13777633099362	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	61488bh1 2562g1 53802cb1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 7686x1

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	-	0	-4	-3	2	3	6	8	5	-6	-1	-6	-12	0	-	8	-9	5	-16	-9	-15	-19

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Quadratic twists for elliptic curve 7686x1

-4	-3	-7
61488bh1	2562g1	53802cb1

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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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