Cremona's table of elliptic curves

4329 = 3² · 13 · 37

Field	Data	Notes
Atkin-Lehner	3- 13+ 37-	Signs for the Atkin-Lehner involutions
Class	4329d	Isogeny class
Conductor	4329	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	3155841 = 38 · 13 · 37	Discriminant
Eigenvalues	1 3-  2 -4  2 13+  8 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-81,-248]	[a1,a2,a3,a4,a6]
Generators	[12:14:1]	Generators of the group modulo torsion
j	81182737/4329	j-invariant
L	4.5115367141431	L(r)(E,1)/r!
Ω	1.5957549497681	Real period
R	2.8272114805589	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69264v1 1443c1 108225u1 56277g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4329d1

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

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Quadratic twists for elliptic curve 4329d1

-4	-3	5	13
69264v1	1443c1	108225u1	56277g1

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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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