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	4	Product of Tamagawa factors cp
Δ	6875 = 54 · 11	Discriminant
Eigenvalues	1  0 5-  0 11+  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-59,190]	[a1,a2,a3,a4,a6]
j	22930509321/6875	j-invariant
L	1.0286698561782	L(r)(E,1)/r!
Ω	4.1146794247128	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	880i3 3520e4 495a3 275a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 55a3

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 55a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
880i3	3520e4	495a3	275a4	2695a3	605b3	9295c4	15895e4	19855b3	29095a4	46255i4	52855j4	75295c4	92455m4	101695a4	121495c4

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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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