Cremona's table of elliptic curves

12152 = 2³ · 7² · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 31-	Signs for the Atkin-Lehner involutions
Class	12152g	Isogeny class
Conductor	12152	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-52285097984 = -1 · 211 · 77 · 31	Discriminant
Eigenvalues	2- -1 -1 7-  4 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-16,-10996]	[a1,a2,a3,a4,a6]
j	-2/217	j-invariant
L	1.0264742853153	L(r)(E,1)/r!
Ω	0.51323714265766	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24304c1 97216u1 109368s1 1736a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12152g1

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	-1	-	4	-4	-2	2	7	1	-	-2	-8	6	-1	-6	-8	-4	3	16	-3	-3	1	9	-8

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Quadratic twists for elliptic curve 12152g1

-4	8	-3	-7
24304c1	97216u1	109368s1	1736a1

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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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