Cremona's table of elliptic curves

3010 = 2 · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5- 7- 43+	Signs for the Atkin-Lehner involutions
Class	3010c	Isogeny class
Conductor	3010	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-240800 = -1 · 25 · 52 · 7 · 43	Discriminant
Eigenvalues	2+ -1 5- 7-  3  6 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-142,596]	[a1,a2,a3,a4,a6]
Generators	[7:-1:1]	Generators of the group modulo torsion
j	-320153881321/240800	j-invariant
L	2.3554011184392	L(r)(E,1)/r!
Ω	3.1008266852041	Real period
R	0.37980212336249	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	24080m1 96320j1 27090bk1 15050q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3010c1

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	-	-	3	6	-4	-5	-8	-5	-5	-1	6	+	0	-8	-6	0	-5	5	6	-6	2	-15	8

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Quadratic twists for elliptic curve 3010c1

-4	8	-3	5	-7	-43
24080m1	96320j1	27090bk1	15050q1	21070c1	129430m1

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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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