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	1012c	Isogeny class
Conductor	1012	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-5387888 = -1 · 24 · 114 · 23	Discriminant
Eigenvalues	2-  1 -4  2 11-  3 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10,109]	[a1,a2,a3,a4,a6]
Generators	[-3:11:1]	Generators of the group modulo torsion
j	-7626496/336743	j-invariant
L	2.4592324467797	L(r)(E,1)/r!
Ω	2.0040351733518	Real period
R	0.30678509033684	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	4048e1 16192a1 9108n1 25300k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1012c1

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	-4	2	-	3	-2	-6	+	-7	-11	8	-9	-4	-7	2	12	-14	8	-15	5	10	6	4	14

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Quadratic twists for elliptic curve 1012c1

-4	8	-3	5	-7	-11	-23
4048e1	16192a1	9108n1	25300k1	49588o1	11132c1	23276b1

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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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