Cremona's table of elliptic curves

10304 = 2⁶ · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	10304w	Isogeny class
Conductor	10304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-513510473728 = -1 · 218 · 7 · 234	Discriminant
Eigenvalues	2-  0 -2 7+  4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1684,-21936]	[a1,a2,a3,a4,a6]
Generators	[426:8832:1]	Generators of the group modulo torsion
j	2014698447/1958887	j-invariant
L	3.3816121261542	L(r)(E,1)/r!
Ω	0.50615086774211	Real period
R	1.6702589789282	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	10304h4 2576l4 92736dx3 72128bw3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10304w4

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

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Quadratic twists for elliptic curve 10304w4

-4	8	-3	-7
10304h4	2576l4	92736dx3	72128bw3

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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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