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	70240320 = 26 · 32 · 5 · 293	Discriminant
Eigenvalues	2+ 3- 5- -4  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2533,-49264]	[a1,a2,a3,a4,a6]
Generators	[67:254:1]	Generators of the group modulo torsion
j	1796316223281481/70240320	j-invariant
L	2.0033437921929	L(r)(E,1)/r!
Ω	0.67299574272548	Real period
R	2.9767555201461	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	6960ba3 27840r3 2610l3 4350p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870c3

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 870c3

-4	8	-3	5	-7	-11	29
6960ba3	27840r3	2610l3	4350p3	42630a3	105270ck3	25230u3

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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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