Cremona's table of elliptic curves

6880 = 2⁵ · 5 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5+ 43+	Signs for the Atkin-Lehner involutions
Class	6880b	Isogeny class
Conductor	6880	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	60032	Modular degree for the optimal curve
Δ	-27834225777356800 = -1 · 212 · 52 · 437	Discriminant
Eigenvalues	2+ -2 5+ -2  3  1 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-128381,-19482581]	[a1,a2,a3,a4,a6]
Generators	[429:2140:1]	Generators of the group modulo torsion
j	-57130682153065984/6795465277675	j-invariant
L	2.3140145881129	L(r)(E,1)/r!
Ω	0.12527219320404	Real period
R	4.6179733285741	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	6880h1 13760k1 61920bv1 34400be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6880b1

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	1	-5	-6	1	-2	11	2	-3	+	12	9	0	-12	15	-12	-4	-8	-3	-6	17

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Quadratic twists for elliptic curve 6880b1

-4	8	-3	5
6880h1	13760k1	61920bv1	34400be1

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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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