Cremona's table of elliptic curves

89376 = 2⁵ · 3 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	89376bn	Isogeny class
Conductor	89376	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	64512	Modular degree for the optimal curve
Δ	-8154487488 = -1 · 26 · 3 · 76 · 192	Discriminant
Eigenvalues	2- 3+ -2 7- -6  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-114,-4332]	[a1,a2,a3,a4,a6]
Generators	[26:98:1]	Generators of the group modulo torsion
j	-21952/1083	j-invariant
L	3.048015475255	L(r)(E,1)/r!
Ω	0.5747313533881	Real period
R	1.3258435723449	Regulator
r	1	Rank of the group of rational points
S	0.99999999750534	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89376cy1 1824k1	Quadratic twists by: -4 -7

Hecke Eigenvalues for elliptic curve 89376bn1

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

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Quadratic twists for elliptic curve 89376bn1

-4	-7
89376cy1	1824k1

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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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