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	10304ba	Isogeny class
Conductor	10304	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	72128 = 26 · 72 · 23	Discriminant
Eigenvalues	2- -2  0 7+  4 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28,-66]	[a1,a2,a3,a4,a6]
Generators	[13:44:1]	Generators of the group modulo torsion
j	39304000/1127	j-invariant
L	2.8987383136748	L(r)(E,1)/r!
Ω	2.0729377320338	Real period
R	2.7967442233113	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	10304be1 5152c2 92736du1 72128ca1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10304ba1

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	-2	0	-4	-	6	2	2	-6	4	-10	6	-6	-4	4	8	-2	0	8	0	4

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Quadratic twists for elliptic curve 10304ba1

-4	8	-3	-7
10304be1	5152c2	92736du1	72128ca1

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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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