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	2178j	Isogeny class
Conductor	2178	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-28579716 = -1 · 22 · 310 · 112	Discriminant
Eigenvalues	2- 3-  1 -4 11-  5  7  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-122,-547]	[a1,a2,a3,a4,a6]
j	-2259169/324	j-invariant
L	2.8522022432074	L(r)(E,1)/r!
Ω	0.71305056080186	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17424bq1 69696cc1 726d1 54450co1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178j1

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
-	-	1	-4	-	5	7	0	0	7	-8	-5	11	8	-4	5	0	2	12	16	6	-4	-8	17	-5

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Quadratic twists for elliptic curve 2178j1

-4	8	-3	5	-7	-11
17424bq1	69696cc1	726d1	54450co1	106722gq1	2178d1

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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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