Cremona's table of elliptic curves

6230 = 2 · 5 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 89+	Signs for the Atkin-Lehner involutions
Class	6230b	Isogeny class
Conductor	6230	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-747911500 = -1 · 22 · 53 · 75 · 89	Discriminant
Eigenvalues	2+  2 5- 7+  3  2 -7  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-982,-12336]	[a1,a2,a3,a4,a6]
j	-104893606034281/747911500	j-invariant
L	2.5571158501211	L(r)(E,1)/r!
Ω	0.42618597502018	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	49840t1 56070x1 31150u1 43610i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6230b1

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
+	2	-	+	3	2	-7	5	9	4	4	5	-9	11	-7	-10	3	-11	12	-5	15	-15	16	+	-1

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Quadratic twists for elliptic curve 6230b1

-4	-3	5	-7
49840t1	56070x1	31150u1	43610i1

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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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