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	2275f	Isogeny class
Conductor	2275	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	210259765625 = 59 · 72 · 133	Discriminant
Eigenvalues	-1 -2 5- 7+  6 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6013,-178608]	[a1,a2,a3,a4,a6]
j	12310389629/107653	j-invariant
L	0.54244476335444	L(r)(E,1)/r!
Ω	0.54244476335444	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	36400cu1 20475bd1 2275g1 15925x1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2275f1

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

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Quadratic twists for elliptic curve 2275f1

-4	-3	5	-7	13
36400cu1	20475bd1	2275g1	15925x1	29575v1

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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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