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	7392j	Isogeny class
Conductor	7392	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	3415104 = 26 · 32 · 72 · 112	Discriminant
Eigenvalues	2- 3+ -2 7+ 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-154,784]	[a1,a2,a3,a4,a6]
Generators	[0:28:1]	Generators of the group modulo torsion
j	6352182208/53361	j-invariant
L	2.8282706957102	L(r)(E,1)/r!
Ω	2.5194329685533	Real period
R	1.1225822361665	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	7392f1 14784w2 22176b1 51744cm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7392j1

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	0	6	8	-10	2	0	12	-6	4	14	4	0	-10	-8	-16	-6	2

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Quadratic twists for elliptic curve 7392j1

-4	8	-3	-7	-11
7392f1	14784w2	22176b1	51744cm1	81312n1

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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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