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	4	Product of Tamagawa factors cp
Δ	107421875 = 510 · 11	Discriminant
Eigenvalues	-1  0 5+  0 11+ -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1480,22272]	[a1,a2,a3,a4,a6]
Generators	[24:0:1]	Generators of the group modulo torsion
j	22930509321/6875	j-invariant
L	1.0969494293484	L(r)(E,1)/r!
Ω	1.8401405798555	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	4400q3 17600j4 2475j3 55a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 275a4

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 275a4

-4	8	-3	5	-7	-11	13	17	-19
4400q3	17600j4	2475j3	55a3	13475e3	3025b3	46475f4	79475k4	99275b4

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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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