Cremona's table of elliptic curves

7252 = 2² · 7² · 37

Field	Data	Notes
Atkin-Lehner	2- 7- 37-	Signs for the Atkin-Lehner involutions
Class	7252b	Isogeny class
Conductor	7252	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-3248896 = -1 · 28 · 73 · 37	Discriminant
Eigenvalues	2-  2 -3 7-  1 -3 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37,-111]	[a1,a2,a3,a4,a6]
j	-65536/37	j-invariant
L	1.8822087040627	L(r)(E,1)/r!
Ω	0.94110435203136	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29008o1 116032e1 65268r1 7252c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7252b1

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	-3	-	1	-3	-2	4	-2	2	-1	-	-6	2	12	9	1	2	-3	9	-4	12	-4	9	-9

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Quadratic twists for elliptic curve 7252b1

-4	8	-3	-7
29008o1	116032e1	65268r1	7252c1

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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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