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	6175c	Isogeny class
Conductor	6175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	912	Modular degree for the optimal curve
Δ	-117325 = -1 · 52 · 13 · 192	Discriminant
Eigenvalues	1 -2 5+  1 -3 13-  1 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-286,1833]	[a1,a2,a3,a4,a6]
Generators	[13:12:1]	Generators of the group modulo torsion
j	-102966775105/4693	j-invariant
L	3.1445016415228	L(r)(E,1)/r!
Ω	3.1246071205021	Real period
R	0.50318352360048	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	98800bx1 55575w1 6175e1 80275e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6175c1

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	-2	+	1	-3	-	1	-	-4	5	5	4	4	-6	3	-3	5	-7	-3	-8	2	10	15	-4	-12

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Quadratic twists for elliptic curve 6175c1

-4	-3	5	13	-19
98800bx1	55575w1	6175e1	80275e1	117325b1

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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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