Cremona's table of elliptic curves

1332 = 2² · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	1332d	Isogeny class
Conductor	1332	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2299394304 = -1 · 28 · 38 · 372	Discriminant
Eigenvalues	2- 3-  2 -4  4 -6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,321,-650]	[a1,a2,a3,a4,a6]
Generators	[150:1850:1]	Generators of the group modulo torsion
j	19600688/12321	j-invariant
L	2.7333656760425	L(r)(E,1)/r!
Ω	0.83808672362218	Real period
R	3.2614353610435	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	5328r2 21312y2 444b2 33300r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1332d2

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
-	-	2	-4	4	-6	-6	-2	-2	2	2	+	-6	-2	4	-10	6	-14	-4	12	-2	-10	0	10	10

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Quadratic twists for elliptic curve 1332d2

-4	8	-3	5	-7	37
5328r2	21312y2	444b2	33300r2	65268j2	49284k2

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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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