Cremona's table of elliptic curves

2075 = 5² · 83

Field	Data	Notes
Atkin-Lehner	5+ 83-	Signs for the Atkin-Lehner involutions
Class	2075c	Isogeny class
Conductor	2075	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-810546875 = -1 · 510 · 83	Discriminant
Eigenvalues	-1 -3 5+ -1  3  6  7  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2730,-54228]	[a1,a2,a3,a4,a6]
j	-143960212521/51875	j-invariant
L	0.66048344176596	L(r)(E,1)/r!
Ω	0.33024172088298	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	33200ba1 18675f1 415a1 101675j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2075c1

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

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Quadratic twists for elliptic curve 2075c1

-4	-3	5	-7
33200ba1	18675f1	415a1	101675j1

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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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