Cremona's table of elliptic curves

4959 = 3² · 19 · 29

Field	Data	Notes
Atkin-Lehner	3+ 19- 29+	Signs for the Atkin-Lehner involutions
Class	4959a	Isogeny class
Conductor	4959	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	431433 = 33 · 19 · 292	Discriminant
Eigenvalues	1 3+  4 -4  6 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-30,63]	[a1,a2,a3,a4,a6]
j	112678587/15979	j-invariant
L	2.8613811553354	L(r)(E,1)/r!
Ω	2.8613811553354	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	79344p1 4959b1 123975g1 94221f1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4959a1

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

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Quadratic twists for elliptic curve 4959a1

-4	-3	5	-19
79344p1	4959b1	123975g1	94221f1

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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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