Cremona's table of elliptic curves

2412 = 2² · 3² · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 67+	Signs for the Atkin-Lehner involutions
Class	2412a	Isogeny class
Conductor	2412	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-27345828096 = -1 · 28 · 313 · 67	Discriminant
Eigenvalues	2- 3-  1 -3  2 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,753,-218]	[a1,a2,a3,a4,a6]
Generators	[2:36:1]	Generators of the group modulo torsion
j	253012016/146529	j-invariant
L	3.1642706392094	L(r)(E,1)/r!
Ω	0.70528239615043	Real period
R	2.243265007379	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	9648o1 38592x1 804d1 60300l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2412a1

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	-3	2	-2	4	-4	-7	8	3	-3	-1	-11	0	-11	3	8	+	-8	-9	0	-11	6	-6

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Quadratic twists for elliptic curve 2412a1

-4	8	-3	5	-7
9648o1	38592x1	804d1	60300l1	118188s1

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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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