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	1143828125 = 57 · 114	Discriminant
Eigenvalues	-1  0 5+  0 11+ -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-730,-7228]	[a1,a2,a3,a4,a6]
Generators	[-16:20:1]	Generators of the group modulo torsion
j	2749884201/73205	j-invariant
L	1.0969494293484	L(r)(E,1)/r!
Ω	0.92007028992775	Real period
R	0.59612262310664	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	4400q4 17600j3 2475j4 55a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 275a3

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 275a3

-4	8	-3	5	-7	-11	13	17	-19
4400q4	17600j3	2475j4	55a2	13475e4	3025b4	46475f3	79475k3	99275b3

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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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