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	5152f	Isogeny class
Conductor	5152	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	13271552 = 29 · 72 · 232	Discriminant
Eigenvalues	2- -2 -2 7- -2  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-64,72]	[a1,a2,a3,a4,a6]
Generators	[-2:14:1]	Generators of the group modulo torsion
j	57512456/25921	j-invariant
L	2.2769988093269	L(r)(E,1)/r!
Ω	2.0092833116773	Real period
R	0.56661964892996	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	5152d2 10304bf2 46368x2 128800e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5152f2

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 5152f2

-4	8	-3	5	-7	-23
5152d2	10304bf2	46368x2	128800e2	36064d2	118496h2

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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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