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	1326c	Isogeny class
Conductor	1326	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	413712 = 24 · 32 · 132 · 17	Discriminant
Eigenvalues	2+ 3-  0 -2 -2 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-21,16]	[a1,a2,a3,a4,a6]
Generators	[-1:6:1]	Generators of the group modulo torsion
j	955671625/413712	j-invariant
L	2.2559210467467	L(r)(E,1)/r!
Ω	2.6942657615496	Real period
R	0.41865228719108	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	10608p1 42432m1 3978g1 33150bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1326c1

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

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Quadratic twists for elliptic curve 1326c1

-4	8	-3	5	-7	13	17
10608p1	42432m1	3978g1	33150bo1	64974k1	17238p1	22542a1

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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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