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	10304o	Isogeny class
Conductor	10304	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	168820736 = 220 · 7 · 23	Discriminant
Eigenvalues	2+ -2  2 7- -6  4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-257,1375]	[a1,a2,a3,a4,a6]
Generators	[13:20:1]	Generators of the group modulo torsion
j	7189057/644	j-invariant
L	3.3980189663333	L(r)(E,1)/r!
Ω	1.7648020422373	Real period
R	1.9254391625848	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	10304s1 322c1 92736cf1 72128t1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10304o1

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

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Quadratic twists for elliptic curve 10304o1

-4	8	-3	-7
10304s1	322c1	92736cf1	72128t1

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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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