Cremona's table of elliptic curves

2275 = 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	5+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	2275d	Isogeny class
Conductor	2275	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-347137451171875 = -1 · 518 · 7 · 13	Discriminant
Eigenvalues	-1  0 5+ 7-  0 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3995,-892128]	[a1,a2,a3,a4,a6]
Generators	[4190:94123:8]	Generators of the group modulo torsion
j	451394172711/22216796875	j-invariant
L	2.0035928041324	L(r)(E,1)/r!
Ω	0.25827420359559	Real period
R	7.7576187487529	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	36400bj3 20475z4 455a4 15925g4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2275d4

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

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Quadratic twists for elliptic curve 2275d4

-4	-3	5	-7	13
36400bj3	20475z4	455a4	15925g4	29575a3

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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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