Cremona's table of elliptic curves

6936 = 2³ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	6936b	Isogeny class
Conductor	6936	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	134640	Modular degree for the optimal curve
Δ	-5714036343725424048 = -1 · 24 · 311 · 1710	Discriminant
Eigenvalues	2+ 3+  0  1  6  5 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-278403,-128062440]	[a1,a2,a3,a4,a6]
Generators	[660062094465:25937296779995:377933067]	Generators of the group modulo torsion
j	-73984000/177147	j-invariant
L	3.9709612087838	L(r)(E,1)/r!
Ω	0.09696549577167	Real period
R	20.476155859268	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	13872j1 55488ba1 20808bc1 6936f1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6936b1

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
+	+	0	1	6	5	+	-5	-8	-6	3	-3	-2	-11	-4	4	-10	-3	7	8	-10	-12	-12	-14	11

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Quadratic twists for elliptic curve 6936b1

-4	8	-3	17
13872j1	55488ba1	20808bc1	6936f1

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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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