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	10304y	Isogeny class
Conductor	10304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	460105384460288 = 225 · 72 · 234	Discriminant
Eigenvalues	2-  2  0 7+  4  0  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-38753,-2736127]	[a1,a2,a3,a4,a6]
Generators	[5707:430836:1]	Generators of the group modulo torsion
j	24553362849625/1755162752	j-invariant
L	6.359135722007	L(r)(E,1)/r!
Ω	0.34180271723199	Real period
R	4.6511740555377	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	10304j2 2576n2 92736dt2 72128cd2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10304y2

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

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Quadratic twists for elliptic curve 10304y2

-4	8	-3	-7
10304j2	2576n2	92736dt2	72128cd2

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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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