Cremona's table of elliptic curves

14504 = 2³ · 7² · 37

Field	Data	Notes
Atkin-Lehner	2+ 7- 37+	Signs for the Atkin-Lehner involutions
Class	14504b	Isogeny class
Conductor	14504	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-7800599296 = -1 · 28 · 77 · 37	Discriminant
Eigenvalues	2+  0 -3 7- -3  5 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,196,4116]	[a1,a2,a3,a4,a6]
Generators	[-10:34:1] [-7:49:1]	Generators of the group modulo torsion
j	27648/259	j-invariant
L	5.7270383799935	L(r)(E,1)/r!
Ω	0.96519841029283	Real period
R	0.37084592652937	Regulator
r	2	Rank of the group of rational points
S	0.99999999999963	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29008c1 116032j1 2072b1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 14504b1

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
+	0	-3	-	-3	5	-6	-4	-8	-8	7	+	-2	-6	-6	1	9	-6	-11	-15	-2	-4	-14	5	-13

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Quadratic twists for elliptic curve 14504b1

-4	8	-7
29008c1	116032j1	2072b1

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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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