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	870c	Isogeny class
Conductor	870	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-356893992600 = -1 · 23 · 3 · 52 · 296	Discriminant
Eigenvalues	2+ 3- 5- -4  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2413,-54112]	[a1,a2,a3,a4,a6]
Generators	[534:2039:8]	Generators of the group modulo torsion
j	-1552876541267401/356893992600	j-invariant
L	2.0033437921929	L(r)(E,1)/r!
Ω	0.33649787136274	Real period
R	5.9535110402923	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	6960ba4 27840r4 2610l4 4350p4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870c4

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

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Quadratic twists for elliptic curve 870c4

-4	8	-3	5	-7	-11	29
6960ba4	27840r4	2610l4	4350p4	42630a4	105270ck4	25230u4

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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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