Cremona's table of elliptic curves

784 = 2⁴ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	784j	Isogeny class
Conductor	784	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	453551299002368 = 215 · 712	Discriminant
Eigenvalues	2- -2  0 7-  0  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-27848,-1475468]	[a1,a2,a3,a4,a6]
Generators	[-124:294:1]	Generators of the group modulo torsion
j	4956477625/941192	j-invariant
L	1.7509775464191	L(r)(E,1)/r!
Ω	0.37443843413795	Real period
R	2.3381381113431	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	98a4 3136y4 7056bp4 19600cp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 784j4

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

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Quadratic twists for elliptic curve 784j4

-4	8	-3	5	-7	-11
98a4	3136y4	7056bp4	19600cp4	112c4	94864cz4

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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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