Cremona's table of elliptic curves

7524 = 2² · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 19-	Signs for the Atkin-Lehner involutions
Class	7524f	Isogeny class
Conductor	7524	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-1053119232 = -1 · 28 · 39 · 11 · 19	Discriminant
Eigenvalues	2- 3-  0  2 11-  5 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1200,-16076]	[a1,a2,a3,a4,a6]
Generators	[101:945:1]	Generators of the group modulo torsion
j	-1024000000/5643	j-invariant
L	4.6599676691718	L(r)(E,1)/r!
Ω	0.40544425285807	Real period
R	2.8733713921967	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	30096t1 120384k1 2508a1 82764g1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7524f1

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	2	-	5	-3	-	-6	0	-4	-10	-6	-4	-6	-3	-3	2	2	-9	8	-1	-3	-9	-10

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Quadratic twists for elliptic curve 7524f1

-4	8	-3	-11
30096t1	120384k1	2508a1	82764g1

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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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