Cremona's table of elliptic curves

1352 = 2³ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	1352a	Isogeny class
Conductor	1352	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-128508962816 = -1 · 211 · 137	Discriminant
Eigenvalues	2+  1  1 -5  2 13+ -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2760,-59344]	[a1,a2,a3,a4,a6]
Generators	[199:2704:1]	Generators of the group modulo torsion
j	-235298/13	j-invariant
L	2.9303046707757	L(r)(E,1)/r!
Ω	0.3282746678176	Real period
R	2.2315951838872	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2704a1 10816f1 12168m1 33800t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1352a1

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	1	-5	2	+	-3	2	4	-6	4	-11	-8	-1	-9	-12	-6	0	-6	-7	2	12	16	10	10

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Quadratic twists for elliptic curve 1352a1

-4	8	-3	5	-7	13
2704a1	10816f1	12168m1	33800t1	66248h1	104a1

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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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