Cremona's table of elliptic curves

41070 = 2 · 3 · 5 · 37²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 37+	Signs for the Atkin-Lehner involutions
Class	41070p	Isogeny class
Conductor	41070	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	1378944	Modular degree for the optimal curve
Δ	-2657484995710348800 = -1 · 29 · 37 · 52 · 377	Discriminant
Eigenvalues	2+ 3- 5- -5 -5  1  5  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-384718,120745856]	[a1,a2,a3,a4,a6]
Generators	[40:10247:1]	Generators of the group modulo torsion
j	-2454365649169/1035763200	j-invariant
L	4.1322024148115	L(r)(E,1)/r!
Ω	0.23984072115021	Real period
R	0.30765971884188	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123210cz1 1110m1	Quadratic twists by: -3 37

Hecke Eigenvalues for elliptic curve 41070p1

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
+	-	-	-5	-5	1	5	3	-3	-6	6	+	0	-4	0	-3	10	-10	-14	6	-9	0	5	-13	4

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Quadratic twists for elliptic curve 41070p1

-3	37
123210cz1	1110m1

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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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