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	2	Product of Tamagawa factors cp
Δ	-651934448 = -1 · 24 · 116 · 23	Discriminant
Eigenvalues	2-  1  0 -4 11+  5 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2278,-42635]	[a1,a2,a3,a4,a6]
Generators	[4035:46585:27]	Generators of the group modulo torsion
j	-81743931616000/40745903	j-invariant
L	2.6109270866055	L(r)(E,1)/r!
Ω	0.34550334663161	Real period
R	3.778439647633	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	4048j2 16192l2 9108o2 25300a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1012b2

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 1012b2

-4	8	-3	5	-7	-11	-23
4048j2	16192l2	9108o2	25300a2	49588f2	11132g2	23276c2

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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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