Cremona's table of elliptic curves

5628 = 2² · 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 67-	Signs for the Atkin-Lehner involutions
Class	5628f	Isogeny class
Conductor	5628	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-30021643008 = -1 · 28 · 36 · 74 · 67	Discriminant
Eigenvalues	2- 3- -4 7-  2 -4  1  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,755,-2161]	[a1,a2,a3,a4,a6]
Generators	[5:42:1]	Generators of the group modulo torsion
j	185673211904/117272043	j-invariant
L	3.759696246943	L(r)(E,1)/r!
Ω	0.67584923072463	Real period
R	0.077262799239671	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22512j1 90048j1 16884n1 39396h1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5628f1

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
-	-	-4	-	2	-4	1	1	1	1	0	-9	0	-6	3	2	13	-2	-	0	-11	4	-4	-7	-12

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Quadratic twists for elliptic curve 5628f1

-4	8	-3	-7
22512j1	90048j1	16884n1	39396h1

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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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