Cremona's table of elliptic curves

784 = 2⁴ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	784d	Isogeny class
Conductor	784	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	4519603984 = 24 · 710	Discriminant
Eigenvalues	2+ -1  1 7- -3  6  5  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-800,8359]	[a1,a2,a3,a4,a6]
j	12544	j-invariant
L	1.3459764273938	L(r)(E,1)/r!
Ω	1.3459764273938	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	392b1 3136w1 7056u1 19600l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 784d1

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
+	-1	1	-	-3	6	5	1	7	2	-5	3	2	4	5	-1	15	5	9	0	-7	-1	12	-7	2

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Quadratic twists for elliptic curve 784d1

-4	8	-3	5	-7	-11
392b1	3136w1	7056u1	19600l1	784a1	94864r1

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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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