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	20	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-68619917011680 = -1 · 25 · 321 · 5 · 41	Discriminant
Eigenvalues	2- 3- 5- -1 -6 -4  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1093,-398581]	[a1,a2,a3,a4,a6]
Generators	[729:19318:1]	Generators of the group modulo torsion
j	198257271191/94128829920	j-invariant
L	5.0833021437398	L(r)(E,1)/r!
Ω	0.2889702827727	Real period
R	0.8795544813406	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	29520ce1 118080bj1 1230b1 18450k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3690u1

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 3690u1

-4	8	-3	5
29520ce1	118080bj1	1230b1	18450k1

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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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