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	3762o	Isogeny class
Conductor	3762	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	-89884121370912 = -1 · 25 · 312 · 114 · 192	Discriminant
Eigenvalues	2- 3-  4  0 11+  4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10103,-598161]	[a1,a2,a3,a4,a6]
j	-156425280396841/123297834528	j-invariant
L	4.6060634986376	L(r)(E,1)/r!
Ω	0.23030317493188	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30096bi2 120384bo2 1254c2 94050s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762o2

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
-	-	4	0	+	4	2	-	-2	-2	-2	0	6	-4	-6	2	12	-6	0	-4	6	-10	8	10	14

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Quadratic twists for elliptic curve 3762o2

-4	8	-3	5	-11	-19
30096bi2	120384bo2	1254c2	94050s2	41382z2	71478s2

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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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