Cremona's table of elliptic curves

4797 = 3² · 13 · 41

Field	Data	Notes
Atkin-Lehner	3- 13- 41+	Signs for the Atkin-Lehner involutions
Class	4797c	Isogeny class
Conductor	4797	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	1428470361279 = 313 · 13 · 413	Discriminant
Eigenvalues	-1 3-  1  2 -1 13-  1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2867,-12828]	[a1,a2,a3,a4,a6]
Generators	[-10:126:1]	Generators of the group modulo torsion
j	3573857582569/1959492951	j-invariant
L	2.7558027551211	L(r)(E,1)/r!
Ω	0.69727822520949	Real period
R	0.98805708234084	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	76752cf1 1599d1 119925o1 62361i1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4797c1

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	2	-1	-	1	0	3	-5	-5	-8	+	-6	-3	3	12	-5	4	0	-16	-13	8	2	13

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Quadratic twists for elliptic curve 4797c1

-4	-3	5	13
76752cf1	1599d1	119925o1	62361i1

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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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