Cremona's table of elliptic curves

51 = 3 · 17

Field	Data	Notes
Atkin-Lehner	3- 17+	Signs for the Atkin-Lehner involutions
Class	51a	Isogeny class
Conductor	51	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-14739 = -1 · 3 · 173	Discriminant
Eigenvalues	0 3-  3 -4 -3 -1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-59,-196]	[a1,a2,a3,a4,a6]
j	-23100424192/14739	j-invariant
L	0.86005901612714	L(r)(E,1)/r!
Ω	0.86005901612714	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	816f2 3264e2 153b2 1275a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 51a2

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	-	3	-4	-3	-1	+	-1	9	6	2	-4	-3	-7	-6	-6	6	8	-4	12	2	-10	-6	0	-16

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Quadratic twists for elliptic curve 51a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
816f2	3264e2	153b2	1275a2	2499d2	6171g2	8619i2	867a2	18411c2	26979p2	42891e2	49011a2	69819e2	85731b2	94299a2	112659h2

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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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