Cremona's table of elliptic curves

55 = 5 · 11

Field	Data	Notes
Atkin-Lehner	5- 11+	Signs for the Atkin-Lehner involutions
Class	55a	Isogeny class
Conductor	55	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	73205 = 5 · 114	Discriminant
Eigenvalues	1  0 5-  0 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-29,-52]	[a1,a2,a3,a4,a6]
j	2749884201/73205	j-invariant
L	1.0286698561782	L(r)(E,1)/r!
Ω	2.0573397123564	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	880i4 3520e3 495a4 275a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 55a2

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	0	-	0	+	2	6	-4	4	6	-8	-2	2	4	-12	-2	4	-10	-16	8	14	8	-4	10	10

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Quadratic twists for elliptic curve 55a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
880i4	3520e3	495a4	275a3	2695a4	605b4	9295c3	15895e3	19855b4	29095a3	46255i3	52855j3	75295c3	92455m3	101695a3	121495c3

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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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