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	510g	Isogeny class
Conductor	510	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-62424000 = -1 · 26 · 33 · 53 · 172	Discriminant
Eigenvalues	2- 3- 5-  2  0 -4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,25,-375]	[a1,a2,a3,a4,a6]
j	1723683599/62424000	j-invariant
L	2.8398724829622	L(r)(E,1)/r!
Ω	0.94662416098739	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	4080v1 16320b1 1530d1 2550d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510g1

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

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Quadratic twists for elliptic curve 510g1

-4	8	-3	5	-7	-11	13	17
4080v1	16320b1	1530d1	2550d1	24990bm1	61710bk1	86190w1	8670n1

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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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