Cremona's table of elliptic curves

1014 = 2 · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	1014a	Isogeny class
Conductor	1014	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-4112784 = -1 · 24 · 32 · 134	Discriminant
Eigenvalues	2+ 3+ -1 -2  2 13+  5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3,-99]	[a1,a2,a3,a4,a6]
Generators	[18:-87:1]	Generators of the group modulo torsion
j	-169/144	j-invariant
L	1.5256284302947	L(r)(E,1)/r!
Ω	1.1126263686041	Real period
R	0.11426630368654	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	8112bc1 32448y1 3042j1 25350cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1014a1

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	-2	2	+	5	-2	6	-9	-4	-11	5	10	2	-1	-8	-11	2	-14	-13	-4	6	2	-2

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Quadratic twists for elliptic curve 1014a1

-4	8	-3	5	-7	-11	13
8112bc1	32448y1	3042j1	25350cv1	49686bf1	122694cj1	1014d1

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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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