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	3075g	Isogeny class
Conductor	3075	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	5400	Modular degree for the optimal curve
Δ	-1955073391875 = -1 · 33 · 54 · 415	Discriminant
Eigenvalues	2 3+ 5-  2 -3 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,2992,22643]	[a1,a2,a3,a4,a6]
Generators	[746:8401:8]	Generators of the group modulo torsion
j	4737871769600/3128117427	j-invariant
L	5.5265477167109	L(r)(E,1)/r!
Ω	0.52048671256555	Real period
R	0.70786920309899	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	49200dz1 9225bb1 3075l2 126075bd1	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 3075g1

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	+	-	2	-3	-4	2	0	-4	-5	-3	-3	-	-4	7	1	0	2	-8	-8	6	10	6	-5	-8

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Quadratic twists for elliptic curve 3075g1

-4	-3	5	41
49200dz1	9225bb1	3075l2	126075bd1

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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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