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	2870d	Isogeny class
Conductor	2870	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	5403406400 = 26 · 52 · 72 · 413	Discriminant
Eigenvalues	2+ -2 5+ 7-  0  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-70344,7175126]	[a1,a2,a3,a4,a6]
Generators	[-92:3633:1]	Generators of the group modulo torsion
j	38494263748526418169/5403406400	j-invariant
L	1.6539828014048	L(r)(E,1)/r!
Ω	1.0584878121782	Real period
R	2.3438854690276	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	22960j1 91840v1 25830bi1 14350p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870d1

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

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Quadratic twists for elliptic curve 2870d1

-4	8	-3	5	-7	41
22960j1	91840v1	25830bi1	14350p1	20090c1	117670a1

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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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