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	4275g	Isogeny class
Conductor	4275	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1669992345703125 = 38 · 59 · 194	Discriminant
Eigenvalues	1 3- 5+ -4 -4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1351692,605208591]	[a1,a2,a3,a4,a6]
j	23977812996389881/146611125	j-invariant
L	0.8429111105202	L(r)(E,1)/r!
Ω	0.4214555552601	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68400fr4 1425h3 855a4 81225bg4	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4275g4

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	-	+	-4	-4	-2	2	+	-4	2	0	6	6	-8	-12	-14	-4	14	4	0	14	16	0	6	10

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Quadratic twists for elliptic curve 4275g4

-4	-3	5	-19
68400fr4	1425h3	855a4	81225bg4

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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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