Cremona's table of elliptic curves

6324 = 2² · 3 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 17- 31-	Signs for the Atkin-Lehner involutions
Class	6324d	Isogeny class
Conductor	6324	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-1239782256 = -1 · 24 · 32 · 172 · 313	Discriminant
Eigenvalues	2- 3-  1 -3  2 -2 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,30,-1683]	[a1,a2,a3,a4,a6]
Generators	[21:93:1]	Generators of the group modulo torsion
j	180472064/77486391	j-invariant
L	4.7424565757605	L(r)(E,1)/r!
Ω	0.71847680547101	Real period
R	0.55005911344295	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	25296k1 101184k1 18972c1 107508a1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6324d1

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	-3	2	-2	-	-5	6	-4	-	-8	7	0	0	6	-9	-4	-12	-3	-2	-8	4	0	-5

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Quadratic twists for elliptic curve 6324d1

-4	8	-3	17
25296k1	101184k1	18972c1	107508a1

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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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