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	5100s	Isogeny class
Conductor	5100	Conductor
∏ cp	102	Product of Tamagawa factors cp
deg	97920	Modular degree for the optimal curve
Δ	-3732150710700000000 = -1 · 28 · 317 · 58 · 172	Discriminant
Eigenvalues	2- 3- 5- -3 -2  5 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-325333,-117328537]	[a1,a2,a3,a4,a6]
Generators	[2258:103275:1]	Generators of the group modulo torsion
j	-38081092648960/37321507107	j-invariant
L	4.2394460406564	L(r)(E,1)/r!
Ω	0.096128908455143	Real period
R	0.43236937925305	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	20400cq1 81600cg1 15300bd1 5100d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5100s1

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	-2	5	-	-7	4	-4	5	-6	2	-5	-12	-6	10	13	-5	-10	-2	-8	4	10	-1

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Quadratic twists for elliptic curve 5100s1

-4	8	-3	5	17
20400cq1	81600cg1	15300bd1	5100d1	86700x1

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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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