Cremona's table of elliptic curves

12616 = 2³ · 19 · 83

Field	Data	Notes
Atkin-Lehner	2- 19+ 83-	Signs for the Atkin-Lehner involutions
Class	12616d	Isogeny class
Conductor	12616	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	25152	Modular degree for the optimal curve
Δ	-3998523517952 = -1 · 210 · 196 · 83	Discriminant
Eigenvalues	2- -1  0  1  5 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-50168,-4309412]	[a1,a2,a3,a4,a6]
Generators	[642642:27600616:343]	Generators of the group modulo torsion
j	-13636809560150500/3904808123	j-invariant
L	3.8519566183606	L(r)(E,1)/r!
Ω	0.15949779394257	Real period
R	6.0376330655512	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	25232a1 100928f1 113544b1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12616d1

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	0	1	5	-4	-3	+	0	-3	11	5	-10	8	6	-4	5	7	2	-8	-4	-6	-	12	-6

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Quadratic twists for elliptic curve 12616d1

-4	8	-3
25232a1	100928f1	113544b1

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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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