Cremona's table of elliptic curves

1175 = 5² · 47

Field	Data	Notes
Atkin-Lehner	5+ 47+	Signs for the Atkin-Lehner involutions
Class	1175a	Isogeny class
Conductor	1175	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	1434326171875 = 515 · 47	Discriminant
Eigenvalues	1  1 5+ -1  3 -3 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-88776,-10188177]	[a1,a2,a3,a4,a6]
Generators	[-377091:203072:2197]	Generators of the group modulo torsion
j	4952031207028849/91796875	j-invariant
L	3.4079955804593	L(r)(E,1)/r!
Ω	0.27658379449965	Real period
R	3.0804367864579	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	18800bb1 75200g1 10575n1 235b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1175a1

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	-1	-4	2	-3	0	4	0	+	-8	-6	5	-4	0	13	-10	-7	14	-12

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Quadratic twists for elliptic curve 1175a1

-4	8	-3	5	-7	-47
18800bb1	75200g1	10575n1	235b1	57575g1	55225b1

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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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