Cremona's table of elliptic curves

6890 = 2 · 5 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2- 5+ 13- 53+	Signs for the Atkin-Lehner involutions
Class	6890l	Isogeny class
Conductor	6890	Conductor
∏ cp	65	Product of Tamagawa factors cp
deg	31200	Modular degree for the optimal curve
Δ	-20150813696000 = -1 · 213 · 53 · 135 · 53	Discriminant
Eigenvalues	2-  1 5+  0 -2 13- -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-125591,17122025]	[a1,a2,a3,a4,a6]
Generators	[206:-51:1]	Generators of the group modulo torsion
j	-219078361234273767409/20150813696000	j-invariant
L	6.4729022034103	L(r)(E,1)/r!
Ω	0.65394306490776	Real period
R	0.15228101063469	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	55120l1 62010s1 34450d1 89570g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890l1

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	-2	-	-2	-1	0	10	4	-6	5	-10	-12	+	-10	-3	12	6	-14	16	-14	-4	-13

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Quadratic twists for elliptic curve 6890l1

-4	-3	5	13
55120l1	62010s1	34450d1	89570g1

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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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