Cremona's table of elliptic curves

3700 = 2² · 5² · 37

Field	Data	Notes
Atkin-Lehner	2- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	3700d	Isogeny class
Conductor	3700	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	92500000000 = 28 · 510 · 37	Discriminant
Eigenvalues	2-  1 5+ -1 -3  6  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1133,863]	[a1,a2,a3,a4,a6]
Generators	[-22:125:1]	Generators of the group modulo torsion
j	40247296/23125	j-invariant
L	3.9631322396828	L(r)(E,1)/r!
Ω	0.91437008817282	Real period
R	2.16713795155	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14800v1 59200i1 33300m1 740c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3700d1

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
-	1	+	-1	-3	6	0	0	-2	-6	0	-	-9	10	-1	-1	0	-12	0	-5	-3	16	-11	0	-8

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Quadratic twists for elliptic curve 3700d1

-4	8	-3	5
14800v1	59200i1	33300m1	740c1

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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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