Cremona's table of elliptic curves

7392 = 2⁵ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	7392k	Isogeny class
Conductor	7392	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2409943269888 = -1 · 29 · 38 · 72 · 114	Discriminant
Eigenvalues	2- 3+ -2 7- 11+  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2744,-92040]	[a1,a2,a3,a4,a6]
Generators	[12260:161595:64]	Generators of the group modulo torsion
j	-4464412682696/4706920449	j-invariant
L	3.1771544315638	L(r)(E,1)/r!
Ω	0.31654383213473	Real period
R	5.018506299961	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	7392e4 14784bl4 22176i2 51744ci2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7392k4

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
-	+	-2	-	+	2	2	4	-4	-6	4	-2	-6	-12	4	6	-4	2	12	12	2	8	-12	-6	18

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Quadratic twists for elliptic curve 7392k4

-4	8	-3	-7	-11
7392e4	14784bl4	22176i2	51744ci2	81312d2

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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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