Cremona's table of elliptic curves

1012 = 2² · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	1012b	Isogeny class
Conductor	1012	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-23555312 = -1 · 24 · 112 · 233	Discriminant
Eigenvalues	2-  1  0 -4 11+  5 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,22,-223]	[a1,a2,a3,a4,a6]
Generators	[14:55:1]	Generators of the group modulo torsion
j	70304000/1472207	j-invariant
L	2.6109270866055	L(r)(E,1)/r!
Ω	1.0365100398948	Real period
R	1.2594798825443	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	4048j1 16192l1 9108o1 25300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1012b1

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	0	-4	+	5	-6	2	-	-9	5	-10	-3	-10	-3	0	12	-4	2	-3	11	8	0	6	8

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Quadratic twists for elliptic curve 1012b1

-4	8	-3	5	-7	-11	-23
4048j1	16192l1	9108o1	25300a1	49588f1	11132g1	23276c1

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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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