Cremona's table of elliptic curves

8075 = 5² · 17 · 19

Field	Data	Notes
Atkin-Lehner	5+ 17- 19+	Signs for the Atkin-Lehner involutions
Class	8075d	Isogeny class
Conductor	8075	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	8280	Modular degree for the optimal curve
Δ	-674432075 = -1 · 52 · 175 · 19	Discriminant
Eigenvalues	-2 -1 5+ -2  2 -6 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3048,65808]	[a1,a2,a3,a4,a6]
j	-125305769758720/26977283	j-invariant
L	0.31396220155513	L(r)(E,1)/r!
Ω	1.5698110077756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	129200cg1 72675v1 8075g2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8075d1

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
-2	-1	+	-2	2	-6	-	+	4	10	7	-7	-3	4	-7	-6	0	2	-12	12	-16	-15	9	0	-17

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Quadratic twists for elliptic curve 8075d1

-4	-3	5
129200cg1	72675v1	8075g2

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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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