Cremona's table of elliptic curves

2870 = 2 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	2870b	Isogeny class
Conductor	2870	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	200900 = 22 · 52 · 72 · 41	Discriminant
Eigenvalues	2+ -2 5+ 7+ -4 -2 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-39,86]	[a1,a2,a3,a4,a6]
Generators	[-6:13:1] [-2:13:1]	Generators of the group modulo torsion
j	6321363049/200900	j-invariant
L	2.2150473655218	L(r)(E,1)/r!
Ω	3.1575227411392	Real period
R	0.35075715158924	Regulator
r	2	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22960m1 91840q1 25830be1 14350u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870b1

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	+	+	-4	-2	-4	-8	-8	0	4	-2	-	-8	-12	-6	4	6	-2	-10	-2	-14	4	-10	-16

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Quadratic twists for elliptic curve 2870b1

-4	8	-3	5	-7	41
22960m1	91840q1	25830be1	14350u1	20090d1	117670h1

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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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