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	3075h	Isogeny class
Conductor	3075	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-1921875 = -1 · 3 · 56 · 41	Discriminant
Eigenvalues	0 3- 5+  4  5  4  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,17,-56]	[a1,a2,a3,a4,a6]
j	32768/123	j-invariant
L	2.6720289269636	L(r)(E,1)/r!
Ω	1.3360144634818	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	49200bs1 9225w1 123b1 126075a1	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 3075h1

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	-	+	4	5	4	5	-2	-4	1	-5	7	+	-7	-7	14	-12	-3	2	-3	-13	-2	2	18	14

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Quadratic twists for elliptic curve 3075h1

-4	-3	5	41
49200bs1	9225w1	123b1	126075a1

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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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