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	7400i	Isogeny class
Conductor	7400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-37483220000000000 = -1 · 211 · 510 · 374	Discriminant
Eigenvalues	2- -1 5+  2 -3  0  7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19792,9246412]	[a1,a2,a3,a4,a6]
Generators	[41:3182:1]	Generators of the group modulo torsion
j	42868750/1874161	j-invariant
L	3.4551842495154	L(r)(E,1)/r!
Ω	0.27672676979183	Real period
R	3.1214763321548	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	14800f1 59200d1 66600t1 7400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7400i1

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	+	2	-3	0	7	-7	-6	8	6	-	-3	4	-4	-6	8	6	-3	0	-3	-10	9	3	-2

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Quadratic twists for elliptic curve 7400i1

-4	8	-3	5
14800f1	59200d1	66600t1	7400c1

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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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