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	3075n	Isogeny class
Conductor	3075	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-80766796875 = -1 · 3 · 58 · 413	Discriminant
Eigenvalues	0 3- 5-  2 -3  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3583,-84881]	[a1,a2,a3,a4,a6]
Generators	[988358:18504611:2744]	Generators of the group modulo torsion
j	-13026426880/206763	j-invariant
L	3.4699828860355	L(r)(E,1)/r!
Ω	0.30823946920939	Real period
R	11.257425581921	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	49200ci2 9225bd2 3075b2 126075o2	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 3075n2

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	-	-	2	-3	2	-6	2	-6	-9	5	-7	+	8	-9	9	6	14	-4	-12	2	-16	-6	-9	8

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Quadratic twists for elliptic curve 3075n2

-4	-3	5	41
49200ci2	9225bd2	3075b2	126075o2

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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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