Cremona's table of elliptic curves

5700 = 2² · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	5700g	Isogeny class
Conductor	5700	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-6768750000 = -1 · 24 · 3 · 58 · 192	Discriminant
Eigenvalues	2- 3+ 5+  4  2 -6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,467,-938]	[a1,a2,a3,a4,a6]
Generators	[21:133:1]	Generators of the group modulo torsion
j	44957696/27075	j-invariant
L	3.7858206737823	L(r)(E,1)/r!
Ω	0.77469380219076	Real period
R	1.6289535569091	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	22800dd1 91200dj1 17100ba1 1140d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5700g1

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
-	+	+	4	2	-6	2	-	-6	8	-8	-10	-4	-4	-6	-12	-8	2	-4	12	10	-8	-2	-12	14

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Quadratic twists for elliptic curve 5700g1

-4	8	-3	5	-19
22800dd1	91200dj1	17100ba1	1140d1	108300cg1

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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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