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	2178a	Isogeny class
Conductor	2178	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	2155125215232 = 212 · 33 · 117	Discriminant
Eigenvalues	2+ 3+  0 -2 11- -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7827,-255051]	[a1,a2,a3,a4,a6]
j	1108717875/45056	j-invariant
L	1.0176897247645	L(r)(E,1)/r!
Ω	0.50884486238225	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bc1 69696k1 2178g3 54450ed1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178a1

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 2178a1

-4	8	-3	5	-7	-11
17424bc1	69696k1	2178g3	54450ed1	106722p1	198c1

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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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