Cremona's table of elliptic curves

1075 = 5² · 43

Field	Data	Notes
Atkin-Lehner	5+ 43-	Signs for the Atkin-Lehner involutions
Class	1075c	Isogeny class
Conductor	1075	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-1075 = -1 · 52 · 43	Discriminant
Eigenvalues	-1  2 5+  4  3  1 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3,-4]	[a1,a2,a3,a4,a6]
j	-121945/43	j-invariant
L	1.7791147132352	L(r)(E,1)/r!
Ω	1.7791147132352	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17200r1 68800s1 9675n1 1075g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1075c1

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	2	+	4	3	1	-2	0	3	0	1	-10	9	-	5	1	1	0	12	6	-14	13	9	-8	9

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Quadratic twists for elliptic curve 1075c1

-4	8	-3	5	-7	-43
17200r1	68800s1	9675n1	1075g1	52675h1	46225h1

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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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