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	16	Product of Tamagawa factors cp
Δ	338950264685868 = 22 · 33 · 1112	Discriminant
Eigenvalues	2- 3+  0 -2 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-17810,233093]	[a1,a2,a3,a4,a6]
Generators	[201:2077:1]	Generators of the group modulo torsion
j	13060888875/7086244	j-invariant
L	4.2024634014843	L(r)(E,1)/r!
Ω	0.47129745298171	Real period
R	2.2291990837724	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	17424bd2 69696l2 2178a4 54450k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178g2

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 2178g2

-4	8	-3	5	-7	-11
17424bd2	69696l2	2178a4	54450k2	106722eo2	198d2

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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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