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	1394c	Isogeny class
Conductor	1394	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1536982811714650112 = 217 · 178 · 412	Discriminant
Eigenvalues	2+  2 -2  0  2 -4 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-770391,-253658539]	[a1,a2,a3,a4,a6]
Generators	[-600454518:-997490363:1061208]	Generators of the group modulo torsion
j	50565952762252669643257/1536982811714650112	j-invariant
L	2.4837761822984	L(r)(E,1)/r!
Ω	0.16144679034585	Real period
R	15.384487836381	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	11152n2 44608f2 12546p2 34850w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394c2

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

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Quadratic twists for elliptic curve 1394c2

-4	8	-3	5	-7	17	41
11152n2	44608f2	12546p2	34850w2	68306q2	23698e2	57154h2

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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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