Cremona's table of elliptic curves

28611 = 3² · 11 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	28611c	Isogeny class
Conductor	28611	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	248832	Modular degree for the optimal curve
Δ	182751402669611193 = 39 · 113 · 178	Discriminant
Eigenvalues	-1 3+  2  2 11+ -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-172154,18286696]	[a1,a2,a3,a4,a6]
Generators	[-23506:1882712:343]	Generators of the group modulo torsion
j	1187648379/384659	j-invariant
L	4.2681187701484	L(r)(E,1)/r!
Ω	0.29536996845044	Real period
R	7.225038470464	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	28611d1 1683d1	Quadratic twists by: -3 17

Hecke Eigenvalues for elliptic curve 28611c1

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
-1	+	2	2	+	-2	+	8	-4	-6	8	2	-6	-8	6	0	-6	4	4	4	0	6	-16	4	-2

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Quadratic twists for elliptic curve 28611c1

-3	17
28611d1	1683d1

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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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