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	2296b	Isogeny class
Conductor	2296	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	514304 = 28 · 72 · 41	Discriminant
Eigenvalues	2-  0 -2 7-  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-671,6690]	[a1,a2,a3,a4,a6]
j	130512259152/2009	j-invariant
L	1.3428404986192	L(r)(E,1)/r!
Ω	2.6856809972383	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4592a1 18368l1 20664g1 57400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2296b1

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	-2	-	0	2	2	0	8	-6	-8	-2	-	4	0	10	12	14	8	0	10	0	12	-14	2

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Quadratic twists for elliptic curve 2296b1

-4	8	-3	5	-7	41
4592a1	18368l1	20664g1	57400b1	16072g1	94136d1

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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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