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	2178d	Isogeny class
Conductor	2178	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-50630710256676 = -1 · 22 · 310 · 118	Discriminant
Eigenvalues	2+ 3-  1  4 11- -5 -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-14724,771876]	[a1,a2,a3,a4,a6]
Generators	[-30:1104:1]	Generators of the group modulo torsion
j	-2259169/324	j-invariant
L	2.6389931636287	L(r)(E,1)/r!
Ω	0.6123417600957	Real period
R	0.35913947292226	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	17424bs1 69696ca1 726i1 54450gi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178d1

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 2178d1

-4	8	-3	5	-7	-11
17424bs1	69696ca1	726i1	54450gi1	106722db1	2178j1

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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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