Cremona's table of elliptic curves

7896 = 2³ · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	7896d	Isogeny class
Conductor	7896	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-114659774208 = -1 · 28 · 34 · 76 · 47	Discriminant
Eigenvalues	2- 3+  0 7+  6  0  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,812,-13916]	[a1,a2,a3,a4,a6]
Generators	[16:54:1]	Generators of the group modulo torsion
j	231002606000/447889743	j-invariant
L	3.7092651136617	L(r)(E,1)/r!
Ω	0.54930255764078	Real period
R	1.6881703271112	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	15792k1 63168bc1 23688c1 55272bb1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7896d1

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	0	2	-8	6	2	-4	-2	-8	-10	-	-6	4	2	10	12	-8	-16	4	-2	-6

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Quadratic twists for elliptic curve 7896d1

-4	8	-3	-7
15792k1	63168bc1	23688c1	55272bb1

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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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