Cremona's table of elliptic curves

510 = 2 · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 17-	Signs for the Atkin-Lehner involutions
Class	510b	Isogeny class
Conductor	510	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	39657600 = 27 · 36 · 52 · 17	Discriminant
Eigenvalues	2+ 3- 5- -2  4  0 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-11603,-482002]	[a1,a2,a3,a4,a6]
j	172735174415217961/39657600	j-invariant
L	1.3800115656084	L(r)(E,1)/r!
Ω	0.46000385520281	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	4080w2 16320h2 1530l2 2550s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510b2

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

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Quadratic twists for elliptic curve 510b2

-4	8	-3	5	-7	-11	13	17
4080w2	16320h2	1530l2	2550s2	24990b2	61710cv2	86190cq2	8670c2

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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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