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	7392b	Isogeny class
Conductor	7392	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1280	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,-54,144]	[a1,a2,a3,a4,a6]
Generators	[-1:14:1]	Generators of the group modulo torsion
j	277167808/53361	j-invariant
L	2.7677624253355	L(r)(E,1)/r!
Ω	2.3796092968966	Real period
R	1.1631163270984	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	7392h1 14784cf2 22176o1 51744bn1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7392b1

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

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Quadratic twists for elliptic curve 7392b1

-4	8	-3	-7	-11
7392h1	14784cf2	22176o1	51744bn1	81312bg1

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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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