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	2178f	Isogeny class
Conductor	2178	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-1411344 = -1 · 24 · 36 · 112	Discriminant
Eigenvalues	2+ 3-  3 -2 11- -5  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,27,-27]	[a1,a2,a3,a4,a6]
Generators	[6:15:1]	Generators of the group modulo torsion
j	24167/16	j-invariant
L	2.5742067067733	L(r)(E,1)/r!
Ω	1.5366415420036	Real period
R	0.41880403405874	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17424cb1 69696dj1 242a1 54450ft1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178f1

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
+	-	3	-2	-	-5	3	-2	-6	-3	2	-7	3	-8	-6	3	0	10	-10	-12	-14	-2	18	9	11

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Quadratic twists for elliptic curve 2178f1

-4	8	-3	5	-7	-11
17424cb1	69696dj1	242a1	54450ft1	106722ds1	2178l1

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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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