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	870g	Isogeny class
Conductor	870	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2207120400 = 24 · 38 · 52 · 292	Discriminant
Eigenvalues	2- 3+ 5-  4  0 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-330,327]	[a1,a2,a3,a4,a6]
j	3975097468321/2207120400	j-invariant
L	2.5341570608475	L(r)(E,1)/r!
Ω	1.2670785304237	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6960bo2 27840bl2 2610c2 4350n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870g2

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	0	-2	2	0	-4	-	4	6	-6	4	8	-10	4	-2	-8	0	10	-4	8	-6	2

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Quadratic twists for elliptic curve 870g2

-4	8	-3	5	-7	-11	29
6960bo2	27840bl2	2610c2	4350n2	42630cz2	105270o2	25230k2

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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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