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	12152d	Isogeny class
Conductor	12152	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1.7970019972631E+21	Discriminant
Eigenvalues	2-  0 -2 7-  2  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17082331,27098309574]	[a1,a2,a3,a4,a6]
Generators	[19647927:-1686951804:2197]	Generators of the group modulo torsion
j	4575904097608151172/14916274366567	j-invariant
L	3.9248342303784	L(r)(E,1)/r!
Ω	0.14932089982408	Real period
R	13.142280266869	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24304g2 97216d2 109368n2 1736b2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12152d2

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
-	0	-2	-	2	4	0	4	-6	-6	+	10	-2	-10	8	6	12	-12	8	-8	8	-14	4	0	-6

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Quadratic twists for elliptic curve 12152d2

-4	8	-3	-7
24304g2	97216d2	109368n2	1736b2

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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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