Cremona's table of elliptic curves

1394 = 2 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 17+ 41+	Signs for the Atkin-Lehner involutions
Class	1394f	Isogeny class
Conductor	1394	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	26132637728 = 25 · 172 · 414	Discriminant
Eigenvalues	2-  2  4  0  2 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-766,-2789]	[a1,a2,a3,a4,a6]
j	49710193744609/26132637728	j-invariant
L	4.8114798645993	L(r)(E,1)/r!
Ω	0.96229597291986	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	11152o2 44608g2 12546h2 34850i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394f2

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	4	0	2	-2	+	-8	-4	8	-8	0	+	-8	0	-2	8	0	4	12	2	-4	0	10	-2

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Quadratic twists for elliptic curve 1394f2

-4	8	-3	5	-7	17	41
11152o2	44608g2	12546h2	34850i2	68306ba2	23698k2	57154o2

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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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