Cremona's table of elliptic curves

7548 = 2² · 3 · 17 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+ 37-	Signs for the Atkin-Lehner involutions
Class	7548c	Isogeny class
Conductor	7548	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	-1056478464 = -1 · 28 · 38 · 17 · 37	Discriminant
Eigenvalues	2- 3+  3 -3  5 -4 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-484,4552]	[a1,a2,a3,a4,a6]
Generators	[34:162:1]	Generators of the group modulo torsion
j	-49081386832/4126869	j-invariant
L	4.0409683143536	L(r)(E,1)/r!
Ω	1.5221887487362	Real period
R	0.44245151569941	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	30192be1 120768bg1 22644i1 128316g1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 7548c1

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
-	+	3	-3	5	-4	+	-5	2	5	-2	-	-12	11	-8	-3	-3	11	-2	-5	-2	-10	-8	14	-5

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Quadratic twists for elliptic curve 7548c1

-4	8	-3	17
30192be1	120768bg1	22644i1	128316g1

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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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