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	5152d	Isogeny class
Conductor	5152	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	10304 = 26 · 7 · 23	Discriminant
Eigenvalues	2-  2 -2 7+  2  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-54,-136]	[a1,a2,a3,a4,a6]
Generators	[284:4776:1]	Generators of the group modulo torsion
j	277167808/161	j-invariant
L	4.674256812928	L(r)(E,1)/r!
Ω	1.7585232275298	Real period
R	5.3161160907656	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	5152f1 10304bb1 46368k1 128800i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5152d1

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

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Quadratic twists for elliptic curve 5152d1

-4	8	-3	5	-7	-23
5152f1	10304bb1	46368k1	128800i1	36064f1	118496k1

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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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