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	2178b	Isogeny class
Conductor	2178	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10024880630821848 = 23 · 312 · 119	Discriminant
Eigenvalues	2+ 3-  0  0 11+  6  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-517842,-143221028]	[a1,a2,a3,a4,a6]
j	8934171875/5832	j-invariant
L	1.423826925066	L(r)(E,1)/r!
Ω	0.17797836563325	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bj2 69696u2 726f2 54450ey2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178b2

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	0	+	6	6	6	-6	-6	4	-2	-6	6	-6	12	12	6	4	6	-12	12	0	6	-10

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Quadratic twists for elliptic curve 2178b2

-4	8	-3	5	-7	-11
17424bj2	69696u2	726f2	54450ey2	106722cb2	2178h2

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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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