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	6175j	Isogeny class
Conductor	6175	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-5217875 = -1 · 53 · 133 · 19	Discriminant
Eigenvalues	1  3 5-  1  2 13- -4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-52,-169]	[a1,a2,a3,a4,a6]
j	-125751501/41743	j-invariant
L	5.2405400232981	L(r)(E,1)/r!
Ω	0.87342333721635	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	98800da1 55575bk1 6175f1 80275u1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6175j1

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	3	-	1	2	-	-4	-	6	0	5	4	-1	4	3	2	0	-7	-8	7	2	10	-15	1	18

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Quadratic twists for elliptic curve 6175j1

-4	-3	5	13	-19
98800da1	55575bk1	6175f1	80275u1	117325q1

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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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