Cremona's table of elliptic curves

6175 = 5² · 13 · 19

Field	Data	Notes
Atkin-Lehner	5- 13- 19+	Signs for the Atkin-Lehner involutions
Class	6175h	Isogeny class
Conductor	6175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-1833203125 = -1 · 58 · 13 · 192	Discriminant
Eigenvalues	1  0 5- -1  5 13-  3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-242,-2459]	[a1,a2,a3,a4,a6]
Generators	[220:3139:1]	Generators of the group modulo torsion
j	-4021785/4693	j-invariant
L	4.5916083235687	L(r)(E,1)/r!
Ω	0.57904320298849	Real period
R	3.9648236089043	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	98800db1 55575be1 6175a1 80275x1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6175h1

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	0	-	-1	5	-	3	+	-6	9	-11	10	-4	0	9	-9	9	-11	-9	12	-4	-8	-7	-12	-12

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Quadratic twists for elliptic curve 6175h1

-4	-3	5	13	-19
98800db1	55575be1	6175a1	80275x1	117325p1

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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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