Cremona's table of elliptic curves

2301 = 3 · 13 · 59

Field	Data	Notes
Atkin-Lehner	3- 13+ 59-	Signs for the Atkin-Lehner involutions
Class	2301b	Isogeny class
Conductor	2301	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	1677429 = 37 · 13 · 59	Discriminant
Eigenvalues	0 3-  1  2 -4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-55,127]	[a1,a2,a3,a4,a6]
Generators	[-1:13:1]	Generators of the group modulo torsion
j	18736316416/1677429	j-invariant
L	3.3292287052501	L(r)(E,1)/r!
Ω	2.5917988205358	Real period
R	0.183503479121	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36816k1 6903e1 57525c1 112749i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2301b1

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	-	1	2	-4	+	-6	4	-9	-8	8	-1	3	-6	6	-2	-	-8	5	0	1	-3	0	-8	-6

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Quadratic twists for elliptic curve 2301b1

-4	-3	5	-7	13
36816k1	6903e1	57525c1	112749i1	29913h1

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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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