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	1394b	Isogeny class
Conductor	1394	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-4492761632 = -1 · 25 · 174 · 412	Discriminant
Eigenvalues	2+  0  2 -2  0  0 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-76,-3216]	[a1,a2,a3,a4,a6]
Generators	[23:71:1]	Generators of the group modulo torsion
j	-48907434393/4492761632	j-invariant
L	2.1343757775001	L(r)(E,1)/r!
Ω	0.60921903740463	Real period
R	3.503462049697	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11152l2 44608c2 12546q2 34850u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394b2

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	2	-2	0	0	+	4	0	-8	-8	-2	+	-4	6	0	-4	14	-4	-14	6	-10	-12	18	-10

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Quadratic twists for elliptic curve 1394b2

-4	8	-3	5	-7	17	41
11152l2	44608c2	12546q2	34850u2	68306l2	23698c2	57154e2

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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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