Cremona's table of elliptic curves

6700 = 2² · 5² · 67

Field	Data	Notes
Atkin-Lehner	2- 5+ 67+	Signs for the Atkin-Lehner involutions
Class	6700b	Isogeny class
Conductor	6700	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-83750000 = -1 · 24 · 57 · 67	Discriminant
Eigenvalues	2- -1 5+ -1 -6 -2 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-158,937]	[a1,a2,a3,a4,a6]
Generators	[12:-25:1] [-12:31:1]	Generators of the group modulo torsion
j	-1755904/335	j-invariant
L	4.361590668246	L(r)(E,1)/r!
Ω	1.8427573182591	Real period
R	0.19724023636708	Regulator
r	2	Rank of the group of rational points
S	0.99999999999975	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26800ba1 107200q1 60300b1 1340c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6700b1

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
-	-1	+	-1	-6	-2	-4	-8	-4	-7	-4	2	-4	11	-8	-3	9	-12	+	12	-14	-6	16	1	11

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Quadratic twists for elliptic curve 6700b1

-4	8	-3	5
26800ba1	107200q1	60300b1	1340c1

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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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