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	6890g	Isogeny class
Conductor	6890	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	101088	Modular degree for the optimal curve
Δ	-287763694985728000 = -1 · 212 · 53 · 139 · 53	Discriminant
Eigenvalues	2+ -2 5-  2 -3 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,164952,1106678]	[a1,a2,a3,a4,a6]
Generators	[297:8587:1]	Generators of the group modulo torsion
j	496363974855285405959/287763694985728000	j-invariant
L	2.2548747661053	L(r)(E,1)/r!
Ω	0.18500499892941	Real period
R	2.0313638182336	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	55120u1 62010bu1 34450p1 89570p1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890g1

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
+	-2	-	2	-3	-	0	-4	-6	9	2	5	3	-13	6	+	0	8	5	-6	-4	-13	15	-6	5

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Quadratic twists for elliptic curve 6890g1

-4	-3	5	13
55120u1	62010bu1	34450p1	89570p1

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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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