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	8	Product of Tamagawa factors cp
Δ	5090492832768 = 210 · 38 · 73 · 472	Discriminant
Eigenvalues	2- 3+  0 7+  6  0  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6048,-142884]	[a1,a2,a3,a4,a6]
Generators	[702:18468:1]	Generators of the group modulo torsion
j	23896313594500/4971184407	j-invariant
L	3.7092651136617	L(r)(E,1)/r!
Ω	0.54930255764078	Real period
R	3.3763406542223	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	15792k2 63168bc2 23688c2 55272bb2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7896d2

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 7896d2

-4	8	-3	-7
15792k2	63168bc2	23688c2	55272bb2

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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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