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	870a	Isogeny class
Conductor	870	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-42480468750 = -1 · 2 · 3 · 512 · 29	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,603,-7869]	[a1,a2,a3,a4,a6]
Generators	[17:79:1]	Generators of the group modulo torsion
j	24185207275559/42480468750	j-invariant
L	1.6315300055282	L(r)(E,1)/r!
Ω	0.59966948242837	Real period
R	0.90690513876706	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	6960bl4 27840bg3 2610k4 4350u4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870a4

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

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Quadratic twists for elliptic curve 870a4

-4	8	-3	5	-7	-11	29
6960bl4	27840bg3	2610k4	4350u4	42630bl3	105270bo3	25230z3

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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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