Cremona's table of elliptic curves

8892 = 2² · 3² · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 19+	Signs for the Atkin-Lehner involutions
Class	8892f	Isogeny class
Conductor	8892	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-752750517168 = -1 · 24 · 33 · 136 · 192	Discriminant
Eigenvalues	2- 3+ -2  0 -2 13-  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1836,51569]	[a1,a2,a3,a4,a6]
Generators	[-40:247:1]	Generators of the group modulo torsion
j	-1584375054336/1742478049	j-invariant
L	3.6726674896489	L(r)(E,1)/r!
Ω	0.81625163270474	Real period
R	0.24996836096017	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	35568bf1 8892e1 115596g1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8892f1

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

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Quadratic twists for elliptic curve 8892f1

-4	-3	13
35568bf1	8892e1	115596g1

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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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