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	48	Product of Tamagawa factors cp
Δ	270030454702272 = 26 · 39 · 118	Discriminant
Eigenvalues	2- 3+  0 -2 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1115885,453986965]	[a1,a2,a3,a4,a6]
Generators	[641:1010:1]	Generators of the group modulo torsion
j	4406910829875/7744	j-invariant
L	4.2024634014843	L(r)(E,1)/r!
Ω	0.47129745298171	Real period
R	0.74306636125746	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	17424bd4 69696l4 2178a2 54450k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178g4

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 2178g4

-4	8	-3	5	-7	-11
17424bd4	69696l4	2178a2	54450k4	106722eo4	198d4

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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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