Cremona's table of elliptic curves

3075 = 3 · 5² · 41

Field	Data	Notes
Atkin-Lehner	3+ 5+ 41+	Signs for the Atkin-Lehner involutions
Class	3075a	Isogeny class
Conductor	3075	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-139163210185546875 = -1 · 3 · 510 · 416	Discriminant
Eigenvalues	0 3+ 5+  1  0  1  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-49583,18460943]	[a1,a2,a3,a4,a6]
Generators	[20793:2998063:1]	Generators of the group modulo torsion
j	-1380482252800/14250312723	j-invariant
L	2.4431211616045	L(r)(E,1)/r!
Ω	0.27895757877839	Real period
R	4.3790191546388	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	49200ct2 9225u2 3075m2 126075s2	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 3075a2

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
0	+	+	1	0	1	0	-7	-6	6	5	-2	+	7	12	6	-12	-13	13	12	-2	8	-12	-12	1

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Quadratic twists for elliptic curve 3075a2

-4	-3	5	41
49200ct2	9225u2	3075m2	126075s2

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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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