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	1394a	Isogeny class
Conductor	1394	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	528	Modular degree for the optimal curve
Δ	2923429888 = 222 · 17 · 41	Discriminant
Eigenvalues	2+  0  0  0  0  4 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-697,6765]	[a1,a2,a3,a4,a6]
Generators	[19:1:1]	Generators of the group modulo torsion
j	37477661819625/2923429888	j-invariant
L	2.0309687002802	L(r)(E,1)/r!
Ω	1.3964967845884	Real period
R	2.9086621934168	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	11152k1 44608b1 12546m1 34850t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394a1

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	0	0	0	4	+	-6	0	6	4	-8	+	-8	-4	4	-4	0	-10	8	-6	-8	0	-6	14

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Quadratic twists for elliptic curve 1394a1

-4	8	-3	5	-7	17	41
11152k1	44608b1	12546m1	34850t1	68306j1	23698b1	57154d1

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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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