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	6890i	Isogeny class
Conductor	6890	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-133349128900 = -1 · 22 · 52 · 132 · 534	Discriminant
Eigenvalues	2+  2 5-  0 -2 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3782,-92824]	[a1,a2,a3,a4,a6]
j	-5985048833061481/133349128900	j-invariant
L	2.431877294937	L(r)(E,1)/r!
Ω	0.30398466186712	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55120y2 62010bp2 34450m2 89570t2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890i2

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	-	0	-2	-	2	2	2	-6	10	10	-6	10	0	-	-6	10	4	-6	6	8	-16	18	2

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Quadratic twists for elliptic curve 6890i2

-4	-3	5	13
55120y2	62010bp2	34450m2	89570t2

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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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