Cremona's table of elliptic curves

3738 = 2 · 3 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 89+	Signs for the Atkin-Lehner involutions
Class	3738c	Isogeny class
Conductor	3738	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	2635174122 = 2 · 3 · 7 · 894	Discriminant
Eigenvalues	2- 3+ -2 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-389,1457]	[a1,a2,a3,a4,a6]
Generators	[1556:4591:64]	Generators of the group modulo torsion
j	6510918987217/2635174122	j-invariant
L	4.0397176427805	L(r)(E,1)/r!
Ω	1.3069400211796	Real period
R	6.18194802717	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	29904e3 119616n3 11214g3 93450x3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3738c4

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

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Quadratic twists for elliptic curve 3738c4

-4	8	-3	5	-7
29904e3	119616n3	11214g3	93450x3	26166z3

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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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