Cremona's table of elliptic curves

15792 = 2⁴ · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	15792d	Isogeny class
Conductor	15792	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-21224448 = -1 · 210 · 32 · 72 · 47	Discriminant
Eigenvalues	2+ 3+ -4 7+  0  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40,256]	[a1,a2,a3,a4,a6]
Generators	[-2:18:1] [0:16:1]	Generators of the group modulo torsion
j	-7086244/20727	j-invariant
L	4.8796213246647	L(r)(E,1)/r!
Ω	1.8950583575971	Real period
R	0.64372969110733	Regulator
r	2	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7896m1 63168de1 47376k1 110544bj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 15792d1

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
+	+	-4	+	0	2	-2	-8	-6	-10	10	-6	-6	-6	-	10	-4	2	-10	-4	0	0	-4	-14	10

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Quadratic twists for elliptic curve 15792d1

-4	8	-3	-7
7896m1	63168de1	47376k1	110544bj1

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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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