Cremona's table of elliptic curves

5152 = 2⁵ · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	5152a	Isogeny class
Conductor	5152	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	13271552 = 29 · 72 · 232	Discriminant
Eigenvalues	2+  2 -4 7+  4  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5640,-161164]	[a1,a2,a3,a4,a6]
Generators	[2388:4186:27]	Generators of the group modulo torsion
j	38758598383688/25921	j-invariant
L	4.2333024315374	L(r)(E,1)/r!
Ω	0.55090077003341	Real period
R	3.8421641988998	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	5152b2 10304v2 46368bn2 128800bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5152a2

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
+	2	-4	+	4	4	-6	2	+	-6	-8	10	6	12	-8	-2	-10	-4	0	8	-14	-8	-14	-2	18

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Quadratic twists for elliptic curve 5152a2

-4	8	-3	5	-7	-23
5152b2	10304v2	46368bn2	128800bd2	36064a2	118496d2

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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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