Cremona's table of elliptic curves

14784 = 2⁶ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	14784bo	Isogeny class
Conductor	14784	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-499580928 = -1 · 216 · 32 · 7 · 112	Discriminant
Eigenvalues	2- 3+  0 7+ 11+ -2 -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,1089]	[a1,a2,a3,a4,a6]
Generators	[-9:24:1] [0:33:1]	Generators of the group modulo torsion
j	-62500/7623	j-invariant
L	5.7830888459438	L(r)(E,1)/r!
Ω	1.3569010594585	Real period
R	1.0654956759065	Regulator
r	2	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14784bi1 3696k1 44352dt1 103488hk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 14784bo1

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	+	+	-2	-8	-6	-8	6	-10	-2	-8	-4	-2	-2	-8	-2	4	4	-4	8	-18	2	-14

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Quadratic twists for elliptic curve 14784bo1

-4	8	-3	-7
14784bi1	3696k1	44352dt1	103488hk1

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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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