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	4275a	Isogeny class
Conductor	4275	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-19037109375 = -1 · 33 · 59 · 192	Discriminant
Eigenvalues	1 3+ 5-  2 -2 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2367,45416]	[a1,a2,a3,a4,a6]
Generators	[20:66:1]	Generators of the group modulo torsion
j	-27818127/361	j-invariant
L	4.5126353327356	L(r)(E,1)/r!
Ω	1.2258508975905	Real period
R	1.8406134635157	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	68400dv1 4275c1 4275d1 81225m1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4275a1

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	-2	-2	2	-	0	6	-4	2	-2	-10	0	-10	0	-10	-4	8	4	-8	-12	-10	-18

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Quadratic twists for elliptic curve 4275a1

-4	-3	5	-19
68400dv1	4275c1	4275d1	81225m1

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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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