Cremona's table of elliptic curves

3042 = 2 · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13-	Signs for the Atkin-Lehner involutions
Class	3042h	Isogeny class
Conductor	3042	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-12812904 = -1 · 23 · 36 · 133	Discriminant
Eigenvalues	2+ 3-  3 -3  0 13-  3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,27,157]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1]	Generators of the group modulo torsion
j	1331/8	j-invariant
L	2.7853339442548	L(r)(E,1)/r!
Ω	1.6248232539243	Real period
R	0.85711905511188	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	24336cg1 97344dn1 338e1 76050fk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3042h1

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
+	-	3	-3	0	-	3	-6	-6	0	0	-3	0	1	3	6	-6	-8	-12	-15	-6	10	-6	-6	-12

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Quadratic twists for elliptic curve 3042h1

-4	8	-3	5	13
24336cg1	97344dn1	338e1	76050fk1	3042o1

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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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