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	2178g	Isogeny class
Conductor	2178	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	1018633402512 = 24 · 33 · 119	Discriminant
Eigenvalues	2- 3+  0 -2 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10550,-411595]	[a1,a2,a3,a4,a6]
Generators	[531:11713:1]	Generators of the group modulo torsion
j	2714704875/21296	j-invariant
L	4.2024634014843	L(r)(E,1)/r!
Ω	0.47129745298171	Real period
R	1.1145995418862	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	17424bd1 69696l1 2178a3 54450k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178g1

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

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Quadratic twists for elliptic curve 2178g1

-4	8	-3	5	-7	-11
17424bd1	69696l1	2178a3	54450k1	106722eo1	198d1

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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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