Cremona's table of elliptic curves

7504 = 2⁴ · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 7+ 67-	Signs for the Atkin-Lehner involutions
Class	7504s	Isogeny class
Conductor	7504	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	7504 = 24 · 7 · 67	Discriminant
Eigenvalues	2- -1  1 7+  4 -1 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	1048576/469	j-invariant
L	3.5967500266115	L(r)(E,1)/r!
Ω	3.7501292769702	Real period
R	0.9591002765423	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	1876a1 30016be1 67536bs1 52528bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504s1

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
-	-1	1	+	4	-1	-4	6	1	-3	-3	5	-9	6	-6	0	-6	10	-	-3	4	-6	4	-14	-2

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Quadratic twists for elliptic curve 7504s1

-4	8	-3	-7
1876a1	30016be1	67536bs1	52528bm1

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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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