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	4	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	-125368768 = -1 · 26 · 7 · 234	Discriminant
Eigenvalues	2+  2 -4 7+  4  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-350,-2464]	[a1,a2,a3,a4,a6]
Generators	[3064:169572:1]	Generators of the group modulo torsion
j	-74299881664/1958887	j-invariant
L	4.2333024315374	L(r)(E,1)/r!
Ω	0.55090077003341	Real period
R	7.6843283977996	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	5152b1 10304v1 46368bn1 128800bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5152a1

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 5152a1

-4	8	-3	5	-7	-23
5152b1	10304v1	46368bn1	128800bd1	36064a1	118496d1

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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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