Cremona's table of elliptic curves

1175 = 5² · 47

Field	Data	Notes
Atkin-Lehner	5+ 47+	Signs for the Atkin-Lehner involutions
Class	1175b	Isogeny class
Conductor	1175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	91796875 = 59 · 47	Discriminant
Eigenvalues	1  1 5+ -1 -3  3  6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-126,273]	[a1,a2,a3,a4,a6]
Generators	[-3:26:1]	Generators of the group modulo torsion
j	13997521/5875	j-invariant
L	3.3923015703272	L(r)(E,1)/r!
Ω	1.7229449905631	Real period
R	0.98444860077003	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	18800ba1 75200f1 10575m1 235a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1175b1

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	1	+	-1	-3	3	6	-7	-4	-10	3	-12	-8	0	+	4	6	5	8	12	-5	14	17	-10	0

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Quadratic twists for elliptic curve 1175b1

-4	8	-3	5	-7	-47
18800ba1	75200f1	10575m1	235a1	57575i1	55225a1

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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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