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	16	Product of Tamagawa factors cp
deg	12672	Modular degree for the optimal curve
Δ	2970335001724992 = 26 · 39 · 119	Discriminant
Eigenvalues	2+ 3-  0  0 11+  6  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-38682,-1293836]	[a1,a2,a3,a4,a6]
j	3723875/1728	j-invariant
L	1.423826925066	L(r)(E,1)/r!
Ω	0.35595673126651	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	17424bj1 69696u1 726f1 54450ey1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178b1

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 2178b1

-4	8	-3	5	-7	-11
17424bj1	69696u1	726f1	54450ey1	106722cb1	2178h1

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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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