Cremona's table of elliptic curves

752 = 2⁴ · 47

Field	Data	Notes
Atkin-Lehner	2- 47-	Signs for the Atkin-Lehner involutions
Class	752a	Isogeny class
Conductor	752	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	18096128 = 213 · 472	Discriminant
Eigenvalues	2-  0  0  0 -2 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-155,714]	[a1,a2,a3,a4,a6]
Generators	[5:8:1]	Generators of the group modulo torsion
j	100544625/4418	j-invariant
L	2.1778815538254	L(r)(E,1)/r!
Ω	2.1590990894351	Real period
R	0.50434960685275	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	94a2 3008b2 6768l2 18800p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 752a2

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	0	0	-2	-4	-2	2	-4	4	-4	2	6	-6	-	2	-12	2	-2	-8	-14	16	16	-10	-14

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Quadratic twists for elliptic curve 752a2

-4	8	-3	5	-7	-11	13	-47
94a2	3008b2	6768l2	18800p2	36848i2	90992t2	127088d2	35344a2

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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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