Cremona's table of elliptic curves

3040 = 2⁵ · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	3040c	Isogeny class
Conductor	3040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	2888000 = 26 · 53 · 192	Discriminant
Eigenvalues	2-  0 5+  2 -4 -4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-173,-872]	[a1,a2,a3,a4,a6]
j	8947094976/45125	j-invariant
L	1.3168001680722	L(r)(E,1)/r!
Ω	1.3168001680722	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3040d1 6080v2 27360l1 15200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3040c1

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
-	0	+	2	-4	-4	6	+	-6	6	8	-4	6	2	10	0	4	-2	16	8	-2	16	6	-10	-12

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Quadratic twists for elliptic curve 3040c1

-4	8	-3	5	-19
3040d1	6080v2	27360l1	15200a1	57760c1

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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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