Cremona's table of elliptic curves

2296 = 2³ · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	2296a	Isogeny class
Conductor	2296	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	28801024 = 211 · 73 · 41	Discriminant
Eigenvalues	2-  1 -3 7+  6  0 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-112,-416]	[a1,a2,a3,a4,a6]
j	76545506/14063	j-invariant
L	1.4850465906884	L(r)(E,1)/r!
Ω	1.4850465906884	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	4592b1 18368b1 20664f1 57400e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2296a1

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	-3	+	6	0	-7	0	8	-3	7	2	+	3	10	9	-6	-1	-2	15	-8	11	6	3	3

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Quadratic twists for elliptic curve 2296a1

-4	8	-3	5	-7	41
4592b1	18368b1	20664f1	57400e1	16072h1	94136g1

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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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