Cremona's table of elliptic curves

4275 = 3² · 5² · 19

Field	Data	Notes
Atkin-Lehner	3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	4275k	Isogeny class
Conductor	4275	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-78128296875 = -1 · 36 · 56 · 193	Discriminant
Eigenvalues	0 3- 5+  1 -3  4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-2100,39406]	[a1,a2,a3,a4,a6]
Generators	[34:85:1]	Generators of the group modulo torsion
j	-89915392/6859	j-invariant
L	3.0951339473135	L(r)(E,1)/r!
Ω	1.0656106734253	Real period
R	0.48409392919028	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	68400ec2 475a2 171b2 81225w2	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4275k2

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	-3	4	-3	-	0	-6	-4	-2	6	1	-3	12	6	-1	4	-6	7	8	12	-12	-8

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Quadratic twists for elliptic curve 4275k2

-4	-3	5	-19
68400ec2	475a2	171b2	81225w2

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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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