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	6175b	Isogeny class
Conductor	6175	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	120000	Modular degree for the optimal curve
Δ	472531982939453125 = 510 · 135 · 194	Discriminant
Eigenvalues	0  3 5+  4 -2 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-197500,-6889844]	[a1,a2,a3,a4,a6]
j	87241870540800/48387275053	j-invariant
L	3.8832036414989	L(r)(E,1)/r!
Ω	0.24270022759368	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	98800bo1 55575k1 6175i1 80275b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6175b1

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 6175b1

-4	-3	5	13	-19
98800bo1	55575k1	6175i1	80275b1	117325i1

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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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