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
deg	432	Modular degree for the optimal curve
Δ	-1421875 = -1 · 56 · 7 · 13	Discriminant
Eigenvalues	0  2 5+ 7+  0 13+  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-183,1018]	[a1,a2,a3,a4,a6]
Generators	[8:1:1]	Generators of the group modulo torsion
j	-43614208/91	j-invariant
L	3.4851582046995	L(r)(E,1)/r!
Ω	2.7009427250227	Real period
R	1.2903488002213	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	36400bz1 20475q1 91b1 15925m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2275a1

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 2275a1

-4	-3	5	-7	13
36400bz1	20475q1	91b1	15925m1	29575i1

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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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