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	16	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	3006720 = 28 · 34 · 5 · 29	Discriminant
Eigenvalues	2- 3+ 5-  4  0 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-250,1415]	[a1,a2,a3,a4,a6]
j	1728432036001/3006720	j-invariant
L	2.5341570608475	L(r)(E,1)/r!
Ω	2.5341570608475	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	6960bo1 27840bl1 2610c1 4350n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870g1

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 870g1

-4	8	-3	5	-7	-11	29
6960bo1	27840bl1	2610c1	4350n1	42630cz1	105270o1	25230k1

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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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