Cremona's table of elliptic curves

1353 = 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	3- 11- 41-	Signs for the Atkin-Lehner involutions
Class	1353d	Isogeny class
Conductor	1353	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	6712233 = 3 · 113 · 412	Discriminant
Eigenvalues	1 3-  2  4 11-  0  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-70,179]	[a1,a2,a3,a4,a6]
j	37159393753/6712233	j-invariant
L	3.3830907052009	L(r)(E,1)/r!
Ω	2.2553938034673	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	21648p1 86592i1 4059a1 33825i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1353d1

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	-	2	4	-	0	6	0	-6	-10	4	2	-	2	0	12	6	6	4	0	-14	-8	-16	-16	-6

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Quadratic twists for elliptic curve 1353d1

-4	8	-3	5	-7	-11	41
21648p1	86592i1	4059a1	33825i1	66297f1	14883i1	55473a1

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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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