Cremona's table of elliptic curves

2178 = 2 · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	2178k	Isogeny class
Conductor	2178	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	85236885954 = 2 · 37 · 117	Discriminant
Eigenvalues	2- 3- -2  4 11-  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-383351,-91261299]	[a1,a2,a3,a4,a6]
j	4824238966273/66	j-invariant
L	3.0698734728872	L(r)(E,1)/r!
Ω	0.19186709205545	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bz3 69696cm4 726c3 54450cq4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178k3

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

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Quadratic twists for elliptic curve 2178k3

-4	8	-3	5	-7	-11
17424bz3	69696cm4	726c3	54450cq4	106722hb4	198a3

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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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