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	336a	Isogeny class
Conductor	336	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-21168 = -1 · 24 · 33 · 72	Discriminant
Eigenvalues	2- 3+  0 7+  6  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7,0]	[a1,a2,a3,a4,a6]
j	2048000/1323	j-invariant
L	1.1949390886861	L(r)(E,1)/r!
Ω	2.3898781773722	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	84a1 1344p1 1008j1 8400ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 336a1

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

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Quadratic twists for elliptic curve 336a1

-4	8	-3	5	-7	-11	13	17	-19
84a1	1344p1	1008j1	8400ci1	2352t1	40656br1	56784bw1	97104co1	121296cm1

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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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