Cremona's table of elliptic curves

870 = 2 · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 29+	Signs for the Atkin-Lehner involutions
Class	870f	Isogeny class
Conductor	870	Conductor
∏ cp	140	Product of Tamagawa factors cp
Δ	-3153750000000 = -1 · 27 · 3 · 510 · 292	Discriminant
Eigenvalues	2- 3+ 5- -4 -4 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,160,85505]	[a1,a2,a3,a4,a6]
Generators	[-7:293:1]	Generators of the group modulo torsion
j	452807907839/3153750000000	j-invariant
L	2.7740230622193	L(r)(E,1)/r!
Ω	0.62848359612881	Real period
R	0.12610957909783	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6960bk2 27840bv2 2610f2 4350l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870f2

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
-	+	-	-4	-4	-4	-2	2	-6	+	0	-2	0	0	0	10	-12	0	-10	16	-10	-16	-4	0	2

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Quadratic twists for elliptic curve 870f2

-4	8	-3	5	-7	-11	29
6960bk2	27840bv2	2610f2	4350l2	42630cx2	105270r2	25230l2

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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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