Cremona's table of elliptic curves

12040 = 2³ · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5- 7- 43-	Signs for the Atkin-Lehner involutions
Class	12040d	Isogeny class
Conductor	12040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	662681600 = 211 · 52 · 7 · 432	Discriminant
Eigenvalues	2+  0 5- 7- -4  2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-227,446]	[a1,a2,a3,a4,a6]
j	631642482/323575	j-invariant
L	1.4255255215985	L(r)(E,1)/r!
Ω	1.4255255215985	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24080c2 96320g2 108360bn2 60200j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12040d2

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
+	0	-	-	-4	2	-4	-6	-6	8	8	-2	10	-	0	0	-12	-10	-8	2	-6	4	6	-4	16

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Quadratic twists for elliptic curve 12040d2

-4	8	-3	5	-7
24080c2	96320g2	108360bn2	60200j2	84280h2

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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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