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	5100t	Isogeny class
Conductor	5100	Conductor
∏ cp	126	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	-346223255343750000 = -1 · 24 · 33 · 59 · 177	Discriminant
Eigenvalues	2- 3- 5- -3  3  0 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,89042,26427713]	[a1,a2,a3,a4,a6]
Generators	[2258:108375:1]	Generators of the group modulo torsion
j	2498351450368/11079144171	j-invariant
L	4.3113748720523	L(r)(E,1)/r!
Ω	0.21719609830016	Real period
R	0.15754086356568	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	20400cr1 81600ch1 15300be1 5100j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5100t1

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
-	-	-	-3	3	0	-	-7	4	1	-10	-1	-3	-10	3	9	-10	-12	10	0	13	2	4	-10	-6

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Quadratic twists for elliptic curve 5100t1

-4	8	-3	5	17
20400cr1	81600ch1	15300be1	5100j1	86700y1

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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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