Cremona's table of elliptic curves

1352 = 2³ · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	1352b	Isogeny class
Conductor	1352	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	2704 = 24 · 132	Discriminant
Eigenvalues	2+  1 -2  1 -1 13+  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	3328	j-invariant
L	2.8293867952658	L(r)(E,1)/r!
Ω	4.2166327937433	Real period
R	0.33550310563729	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	2704c1 10816g1 12168o1 33800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1352b1

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

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Quadratic twists for elliptic curve 1352b1

-4	8	-3	5	-7	13
2704c1	10816g1	12168o1	33800s1	66248i1	1352c1

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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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