Cremona's table of elliptic curves

37128 = 2³ · 3 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	37128be	Isogeny class
Conductor	37128	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	63816314700063744 = 210 · 312 · 74 · 132 · 172	Discriminant
Eigenvalues	2- 3- -2 7+  0 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-206024,33810816]	[a1,a2,a3,a4,a6]
Generators	[-80:7056:1]	Generators of the group modulo torsion
j	944450732945420068/62320619824281	j-invariant
L	5.7811865518675	L(r)(E,1)/r!
Ω	0.34289768337931	Real period
R	1.4049833794185	Regulator
r	1	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	74256t2 111384s2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 37128be2

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

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Quadratic twists for elliptic curve 37128be2

-4	-3
74256t2	111384s2

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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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