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	2275a	Isogeny class
Conductor	2275	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-11774546875 = -1 · 56 · 73 · 133	Discriminant
Eigenvalues	0  2 5+ 7+  0 13+  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,317,4643]	[a1,a2,a3,a4,a6]
Generators	[33:223:1]	Generators of the group modulo torsion
j	224755712/753571	j-invariant
L	3.4851582046995	L(r)(E,1)/r!
Ω	0.90031424167424	Real period
R	3.8710464006639	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	36400bz2 20475q2 91b2 15925m2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2275a2

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	2	+	+	0	+	6	-7	-3	-9	5	-2	-6	1	-3	9	0	-10	-14	-6	-11	-1	-3	15	1

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Quadratic twists for elliptic curve 2275a2

-4	-3	5	-7	13
36400bz2	20475q2	91b2	15925m2	29575i2

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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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