Cremona's table of elliptic curves

275 = 5² · 11

Field	Data	Notes
Atkin-Lehner	5+ 11+	Signs for the Atkin-Lehner involutions
Class	275a	Isogeny class
Conductor	275	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	47265625 = 58 · 112	Discriminant
Eigenvalues	-1  0 5+  0 11+ -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-105,272]	[a1,a2,a3,a4,a6]
Generators	[0:16:1]	Generators of the group modulo torsion
j	8120601/3025	j-invariant
L	1.0969494293484	L(r)(E,1)/r!
Ω	1.8401405798555	Real period
R	1.1922452462133	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4400q2 17600j2 2475j2 55a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 275a2

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

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Quadratic twists for elliptic curve 275a2

-4	8	-3	5	-7	-11	13	17	-19
4400q2	17600j2	2475j2	55a1	13475e2	3025b2	46475f2	79475k2	99275b2

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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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