Cremona's table of elliptic curves

3212 = 2² · 11 · 73

Field	Data	Notes
Atkin-Lehner	2- 11- 73+	Signs for the Atkin-Lehner involutions
Class	3212b	Isogeny class
Conductor	3212	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1176	Modular degree for the optimal curve
Δ	-15006464 = -1 · 28 · 11 · 732	Discriminant
Eigenvalues	2- -3  3 -4 11-  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16,-188]	[a1,a2,a3,a4,a6]
Generators	[28:146:1]	Generators of the group modulo torsion
j	-1769472/58619	j-invariant
L	2.2720727225158	L(r)(E,1)/r!
Ω	0.96502251439461	Real period
R	0.39240409569461	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	12848b1 51392c1 28908e1 80300f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3212b1

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
-	-3	3	-4	-	0	0	-4	1	6	3	-5	-6	-2	0	-6	5	6	3	-1	+	8	6	3	9

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Quadratic twists for elliptic curve 3212b1

-4	8	-3	5	-11
12848b1	51392c1	28908e1	80300f1	35332b1

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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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