Cremona's table of elliptic curves

7400 = 2³ · 5² · 37

Field	Data	Notes
Atkin-Lehner	2- 5+ 37+	Signs for the Atkin-Lehner involutions
Class	7400f	Isogeny class
Conductor	7400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	740000000 = 28 · 57 · 37	Discriminant
Eigenvalues	2-  2 5+ -2  0  6  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1508,23012]	[a1,a2,a3,a4,a6]
j	94875856/185	j-invariant
L	3.2061129506816	L(r)(E,1)/r!
Ω	1.6030564753408	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	14800d1 59200bg1 66600o1 1480c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7400f1

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
-	2	+	-2	0	6	2	6	4	-2	-6	+	-6	-8	6	10	14	6	14	8	6	-14	-2	-6	-2

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Quadratic twists for elliptic curve 7400f1

-4	8	-3	5
14800d1	59200bg1	66600o1	1480c1

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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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