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	1332b	Isogeny class
Conductor	1332	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-591408 = -1 · 24 · 33 · 372	Discriminant
Eigenvalues	2- 3+ -2  0  4 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36,-91]	[a1,a2,a3,a4,a6]
Generators	[19:78:1]	Generators of the group modulo torsion
j	-11943936/1369	j-invariant
L	2.4840088973789	L(r)(E,1)/r!
Ω	0.9682844922351	Real period
R	2.5653709393249	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	5328m1 21312a1 1332a1 33300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1332b1

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	0	4	-6	6	-4	-6	6	-8	-	0	4	-8	-12	-14	-2	12	0	-14	0	4	10	-18

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Quadratic twists for elliptic curve 1332b1

-4	8	-3	5	-7	37
5328m1	21312a1	1332a1	33300a1	65268a1	49284f1

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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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