Cremona's table of elliptic curves

3690 = 2 · 3² · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 41-	Signs for the Atkin-Lehner involutions
Class	3690u	Isogeny class
Conductor	3690	Conductor
∏ cp	540	Product of Tamagawa factors cp
Δ	-50008671793152000 = -1 · 215 · 311 · 53 · 413	Discriminant
Eigenvalues	2- 3- 5- -1 -6 -4  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-9842,10768241]	[a1,a2,a3,a4,a6]
Generators	[-81:3361:1]	Generators of the group modulo torsion
j	-144612187806169/68599001088000	j-invariant
L	5.0833021437398	L(r)(E,1)/r!
Ω	0.2889702827727	Real period
R	0.29318482711353	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	29520ce2 118080bj2 1230b2 18450k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3690u2

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	-6	-4	0	5	3	-6	-1	-7	-	11	-12	-9	-9	8	-4	-12	2	-16	-12	15	2

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Quadratic twists for elliptic curve 3690u2

-4	8	-3	5
29520ce2	118080bj2	1230b2	18450k2

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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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