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	10304bg	Isogeny class
Conductor	10304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	217441107968 = 223 · 72 · 232	Discriminant
Eigenvalues	2- -2  2 7- -2  4 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11137,-455553]	[a1,a2,a3,a4,a6]
Generators	[287:4480:1]	Generators of the group modulo torsion
j	582810602977/829472	j-invariant
L	3.5956471437447	L(r)(E,1)/r!
Ω	0.46477351252904	Real period
R	1.9340856604431	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	10304d2 2576p2 92736fn2 72128bj2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10304bg2

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	2	-	-2	4	-6	0	+	2	-4	0	6	6	0	12	-10	-2	-2	-8	2	-8	-16	6	-2

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Quadratic twists for elliptic curve 10304bg2

-4	8	-3	-7
10304d2	2576p2	92736fn2	72128bj2

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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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