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	2178c	Isogeny class
Conductor	2178	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	330037222413888 = 26 · 37 · 119	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-87687,-9934083]	[a1,a2,a3,a4,a6]
Generators	[1246:41969:1]	Generators of the group modulo torsion
j	57736239625/255552	j-invariant
L	2.2422631081335	L(r)(E,1)/r!
Ω	0.27751162495467	Real period
R	2.0199722340458	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	17424bm3 69696bn3 726h3 54450fr3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178c3

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

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Quadratic twists for elliptic curve 2178c3

-4	8	-3	5	-7	-11
17424bm3	69696bn3	726h3	54450fr3	106722cu3	198b3

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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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