Cremona's table of elliptic curves

4785 = 3 · 5 · 11 · 29

Field	Data	Notes
Atkin-Lehner	3+ 5- 11+ 29-	Signs for the Atkin-Lehner involutions
Class	4785a	Isogeny class
Conductor	4785	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-412703290692825 = -1 · 3 · 52 · 11 · 298	Discriminant
Eigenvalues	-1 3+ 5-  0 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-10335,1053462]	[a1,a2,a3,a4,a6]
Generators	[-93:1151:1]	Generators of the group modulo torsion
j	-122083727651299441/412703290692825	j-invariant
L	2.0791178087652	L(r)(E,1)/r!
Ω	0.46602327299688	Real period
R	4.4614033874207	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	76560cj3 14355d4 23925s3 52635d3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4785a4

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

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Quadratic twists for elliptic curve 4785a4

-4	-3	5	-11
76560cj3	14355d4	23925s3	52635d3

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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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