Cremona's table of elliptic curves

3762 = 2 · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	3762f	Isogeny class
Conductor	3762	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	609444 = 22 · 36 · 11 · 19	Discriminant
Eigenvalues	2+ 3- -2  2 11+ -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-33,-55]	[a1,a2,a3,a4,a6]
Generators	[-4:3:1]	Generators of the group modulo torsion
j	5545233/836	j-invariant
L	2.413042759109	L(r)(E,1)/r!
Ω	2.0092054526888	Real period
R	1.2009935349716	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30096bg1 120384bj1 418a1 94050cz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762f1

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

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Quadratic twists for elliptic curve 3762f1

-4	8	-3	5	-11	-19
30096bg1	120384bj1	418a1	94050cz1	41382cb1	71478ca1

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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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