Cremona's table of elliptic curves

336 = 2⁴ · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	336f	Isogeny class
Conductor	336	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	16128 = 28 · 32 · 7	Discriminant
Eigenvalues	2- 3-  4 7- -2 -6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36,72]	[a1,a2,a3,a4,a6]
j	20720464/63	j-invariant
L	1.9657966013277	L(r)(E,1)/r!
Ω	3.9315932026554	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	84b2 1344o2 1008m2 8400bj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 336f2

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

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Quadratic twists for elliptic curve 336f2

-4	8	-3	5	-7	-11	13	17	-19
84b2	1344o2	1008m2	8400bj2	2352p2	40656cu2	56784ct2	97104br2	121296cl2

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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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