Cremona's table of elliptic curves

1326 = 2 · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 17+	Signs for the Atkin-Lehner involutions
Class	1326a	Isogeny class
Conductor	1326	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3200	Modular degree for the optimal curve
Δ	29358565696512 = 210 · 310 · 134 · 17	Discriminant
Eigenvalues	2+ 3+  0  2 -4 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-19110,-990828]	[a1,a2,a3,a4,a6]
Generators	[732:19074:1]	Generators of the group modulo torsion
j	771864882375147625/29358565696512	j-invariant
L	1.8069131773062	L(r)(E,1)/r!
Ω	0.40700272414775	Real period
R	2.2197802005992	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	10608t1 42432w1 3978i1 33150cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1326a1

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	2	-4	+	+	4	-2	-4	-2	0	2	4	-4	6	-4	4	4	-2	-10	-6	-4	-10	-14

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Quadratic twists for elliptic curve 1326a1

-4	8	-3	5	-7	13	17
10608t1	42432w1	3978i1	33150cf1	64974bb1	17238i1	22542i1

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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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