Cremona's table of elliptic curves

2300 = 2² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	2300c	Isogeny class
Conductor	2300	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-460000000 = -1 · 28 · 57 · 23	Discriminant
Eigenvalues	2-  0 5+  1  6 -6 -7  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-200,-1500]	[a1,a2,a3,a4,a6]
Generators	[20:50:1]	Generators of the group modulo torsion
j	-221184/115	j-invariant
L	3.1529591934669	L(r)(E,1)/r!
Ω	0.61960095621161	Real period
R	0.42405776947484	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	9200r1 36800t1 20700h1 460a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2300c1

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	6	-6	-7	2	-	-5	1	5	-7	-8	-8	-3	13	-8	9	7	2	-12	5	-12	-2

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Quadratic twists for elliptic curve 2300c1

-4	8	-3	5	-7	-23
9200r1	36800t1	20700h1	460a1	112700m1	52900c1

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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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