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	2301a	Isogeny class
Conductor	2301	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-559143 = -1 · 36 · 13 · 59	Discriminant
Eigenvalues	-1 3+  0  2 -4 13-  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,7,38]	[a1,a2,a3,a4,a6]
Generators	[-2:5:1]	Generators of the group modulo torsion
j	37595375/559143	j-invariant
L	1.7704941082726	L(r)(E,1)/r!
Ω	2.1633921567179	Real period
R	1.6367759333644	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	36816u1 6903f1 57525i1 112749o1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2301a1

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
-1	+	0	2	-4	-	6	-6	-8	6	0	6	12	2	0	-2	-	2	-16	12	10	-4	-12	-18	-2

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Quadratic twists for elliptic curve 2301a1

-4	-3	5	-7	13
36816u1	6903f1	57525i1	112749o1	29913a1

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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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