Cremona's table of elliptic curves

5100 = 2² · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	5100f	Isogeny class
Conductor	5100	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-165813750000 = -1 · 24 · 33 · 57 · 173	Discriminant
Eigenvalues	2- 3+ 5+ -5  3 -2 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2158,-42563]	[a1,a2,a3,a4,a6]
j	-4447738624/663255	j-invariant
L	0.69471441360445	L(r)(E,1)/r!
Ω	0.34735720680223	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20400dg1 81600dj1 15300z1 1020g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5100f1

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
-	+	+	-5	3	-2	+	-7	6	-3	2	-11	-3	-8	9	-9	12	-10	-8	12	7	-10	12	-12	-2

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Quadratic twists for elliptic curve 5100f1

-4	8	-3	5	17
20400dg1	81600dj1	15300z1	1020g1	86700bo1

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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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