Cremona's table of elliptic curves

6325 = 5² · 11 · 23

Field	Data	Notes
Atkin-Lehner	5- 11- 23+	Signs for the Atkin-Lehner involutions
Class	6325f	Isogeny class
Conductor	6325	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	11958203125 = 58 · 113 · 23	Discriminant
Eigenvalues	0  1 5- -1 11-  2  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-583,1119]	[a1,a2,a3,a4,a6]
Generators	[-198:249:8]	Generators of the group modulo torsion
j	56197120/30613	j-invariant
L	3.7311860402514	L(r)(E,1)/r!
Ω	1.1063924458423	Real period
R	3.3723892948408	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	101200cg1 56925bc1 6325c1 69575w1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6325f1

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

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Quadratic twists for elliptic curve 6325f1

-4	-3	5	-11
101200cg1	56925bc1	6325c1	69575w1

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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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