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	5100h	Isogeny class
Conductor	5100	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	387281250000 = 24 · 36 · 59 · 17	Discriminant
Eigenvalues	2- 3+ 5-  0  0  0 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1833,4662]	[a1,a2,a3,a4,a6]
Generators	[-22:184:1]	Generators of the group modulo torsion
j	21807104/12393	j-invariant
L	3.2554434699645	L(r)(E,1)/r!
Ω	0.81669829217368	Real period
R	3.9861029478829	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	20400dn1 81600ee1 15300bf1 5100p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5100h1

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	0	0	+	-4	8	-8	2	-2	0	4	-6	6	-4	6	8	-12	2	-10	2	2	-6

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Quadratic twists for elliptic curve 5100h1

-4	8	-3	5	17
20400dn1	81600ee1	15300bf1	5100p1	86700bu1

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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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