Cremona's table of elliptic curves

6944 = 2⁵ · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	6944c	Isogeny class
Conductor	6944	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-5444096 = -1 · 29 · 73 · 31	Discriminant
Eigenvalues	2+  1  1 7-  0  0 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,136]	[a1,a2,a3,a4,a6]
Generators	[-6:14:1]	Generators of the group modulo torsion
j	-14172488/10633	j-invariant
L	5.1804026844587	L(r)(E,1)/r!
Ω	2.216869973697	Real period
R	0.38946824020082	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	6944e1 13888j1 62496by1 48608c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6944c1

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	1	-	0	0	-2	6	-1	-9	-	-6	0	-10	-9	-2	-8	8	-11	12	5	-11	15	1	-4

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Quadratic twists for elliptic curve 6944c1

-4	8	-3	-7
6944e1	13888j1	62496by1	48608c1

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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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