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	1353b	Isogeny class
Conductor	1353	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	4493313 = 35 · 11 · 412	Discriminant
Eigenvalues	-1 3+  2  0 11-  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-42,-42]	[a1,a2,a3,a4,a6]
j	8205738913/4493313	j-invariant
L	1.0016831005425	L(r)(E,1)/r!
Ω	2.0033662010849	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	21648ba1 86592bb1 4059b1 33825r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1353b1

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	0	-	4	-6	4	6	2	-4	2	+	-2	0	4	2	6	12	0	-6	4	16	8	-6

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Quadratic twists for elliptic curve 1353b1

-4	8	-3	5	-7	-11	41
21648ba1	86592bb1	4059b1	33825r1	66297t1	14883e1	55473n1

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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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