Cremona's table of elliptic curves

3312 = 2⁴ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 23+	Signs for the Atkin-Lehner involutions
Class	3312b	Isogeny class
Conductor	3312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	103016448 = 211 · 37 · 23	Discriminant
Eigenvalues	2+ 3-  2  4  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26499,1660322]	[a1,a2,a3,a4,a6]
j	1378334691074/69	j-invariant
L	2.8249875775606	L(r)(E,1)/r!
Ω	1.4124937887803	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1656c3 13248bh4 1104a3 82800bq4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312b4

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	0	-2	2	4	+	2	8	2	-10	4	0	-6	12	2	12	-16	10	4	0	-6	-14

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Quadratic twists for elliptic curve 3312b4

-4	8	-3	5	-23
1656c3	13248bh4	1104a3	82800bq4	76176y4

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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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