Cremona's table of elliptic curves

6832 = 2⁴ · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 7+ 61+	Signs for the Atkin-Lehner involutions
Class	6832a	Isogeny class
Conductor	6832	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	1626999808 = 210 · 7 · 613	Discriminant
Eigenvalues	2+  1  2 7+  3  0 -5  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1912,31492]	[a1,a2,a3,a4,a6]
Generators	[24:2:1]	Generators of the group modulo torsion
j	755291402212/1588867	j-invariant
L	5.2626775627782	L(r)(E,1)/r!
Ω	1.5019941916588	Real period
R	1.7518967756348	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	3416a1 27328w1 61488b1 47824b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6832a1

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	2	+	3	0	-5	5	-5	2	-10	-6	4	-11	1	8	-12	+	-15	3	4	-1	-15	-5	10

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Quadratic twists for elliptic curve 6832a1

-4	8	-3	-7
3416a1	27328w1	61488b1	47824b1

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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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