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	870b	Isogeny class
Conductor	870	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1291776000000 = 215 · 3 · 56 · 292	Discriminant
Eigenvalues	2+ 3- 5+  2 -6 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-524364,-146193014]	[a1,a2,a3,a4,a6]
Generators	[-143457230:71990549:343000]	Generators of the group modulo torsion
j	15944875212653044225849/1291776000000	j-invariant
L	1.9885607214778	L(r)(E,1)/r!
Ω	0.17741545079431	Real period
R	11.208497977909	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	6960w4 27840w4 2610m4 4350s4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870b4

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
+	-	+	2	-6	-4	-6	-4	0	-	2	2	0	-4	0	6	-12	-4	8	0	2	-10	18	0	-10

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Quadratic twists for elliptic curve 870b4

-4	8	-3	5	-7	-11	29
6960w4	27840w4	2610m4	4350s4	42630bb4	105270bt4	25230o4

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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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