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	6175i	Isogeny class
Conductor	6175	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	24000	Modular degree for the optimal curve
Δ	30242046908125 = 54 · 135 · 194	Discriminant
Eigenvalues	0 -3 5- -4 -2 13- -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-7900,-55119]	[a1,a2,a3,a4,a6]
Generators	[-85:47:1] [-35:422:1]	Generators of the group modulo torsion
j	87241870540800/48387275053	j-invariant
L	2.7338031535168	L(r)(E,1)/r!
Ω	0.54269420705415	Real period
R	0.083957752450144	Regulator
r	2	Rank of the group of rational points
S	0.9999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	98800cz1 55575bf1 6175b1 80275n1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6175i1

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	-3	-	-4	-2	-	-2	-	-5	1	-4	-2	-6	1	-12	3	14	-1	-6	-14	-8	-17	-2	-8	-18

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Quadratic twists for elliptic curve 6175i1

-4	-3	5	13	-19
98800cz1	55575bf1	6175b1	80275n1	117325n1

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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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