Cremona's table of elliptic curves

784 = 2⁴ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	784a	Isogeny class
Conductor	784	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	38416 = 24 · 74	Discriminant
Eigenvalues	2+  1 -1 7+ -3 -6 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,-29]	[a1,a2,a3,a4,a6]
Generators	[-3:1:1]	Generators of the group modulo torsion
j	12544	j-invariant
L	2.3969872725452	L(r)(E,1)/r!
Ω	2.3868312844838	Real period
R	1.0042550087756	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	392c1 3136p1 7056o1 19600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 784a1

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 784a1

-4	8	-3	5	-7	-11
392c1	3136p1	7056o1	19600c1	784d1	94864c1

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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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