Cremona's table of elliptic curves

2856 = 2³ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	2856f	Isogeny class
Conductor	2856	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	130507776 = 210 · 32 · 72 · 172	Discriminant
Eigenvalues	2- 3+  2 7- -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-152,-420]	[a1,a2,a3,a4,a6]
Generators	[22:80:1]	Generators of the group modulo torsion
j	381775972/127449	j-invariant
L	3.2109929270268	L(r)(E,1)/r!
Ω	1.3954314667294	Real period
R	2.3010753330314	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	5712j2 22848bi2 8568g2 71400bm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2856f2

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

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Quadratic twists for elliptic curve 2856f2

-4	8	-3	5	-7	17
5712j2	22848bi2	8568g2	71400bm2	19992ba2	48552bc2

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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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