Cremona's table of elliptic curves

4738 = 2 · 23 · 103

Field	Data	Notes
Atkin-Lehner	2+ 23- 103-	Signs for the Atkin-Lehner involutions
Class	4738b	Isogeny class
Conductor	4738	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-5382457310314496 = -1 · 232 · 233 · 103	Discriminant
Eigenvalues	2+ -1  1  3  0 -2 -4  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,42018,1229812]	[a1,a2,a3,a4,a6]
Generators	[35580:735874:125]	Generators of the group modulo torsion
j	8203774086256797719/5382457310314496	j-invariant
L	2.6247019333193	L(r)(E,1)/r!
Ω	0.26868805816106	Real period
R	1.6280973751267	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	37904d1 42642m1 118450i1 108974a1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4738b1

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
+	-1	1	3	0	-2	-4	5	-	-3	5	-1	-7	-4	4	6	6	-14	-8	-9	4	12	-13	-10	8

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Quadratic twists for elliptic curve 4738b1

-4	-3	5	-23
37904d1	42642m1	118450i1	108974a1

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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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