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	5628a	Isogeny class
Conductor	5628	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	764640	Modular degree for the optimal curve
Δ	-1.4264773789802E+22	Discriminant
Eigenvalues	2- 3+ -4 7- -4 -6  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2155475,-5616471494]	[a1,a2,a3,a4,a6]
Generators	[1410:14966:1]	Generators of the group modulo torsion
j	69220143982029586694144/891548361862595049123	j-invariant
L	2.2707258159743	L(r)(E,1)/r!
Ω	0.061388111560761	Real period
R	6.1649445314473	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	22512s1 90048bb1 16884h1 39396l1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5628a1

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

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Quadratic twists for elliptic curve 5628a1

-4	8	-3	-7
22512s1	90048bb1	16884h1	39396l1

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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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