Cremona's table of elliptic curves

43245 = 3² · 5 · 31²

Field	Data	Notes
Atkin-Lehner	3- 5- 31-	Signs for the Atkin-Lehner involutions
Class	43245n	Isogeny class
Conductor	43245	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	50400	Modular degree for the optimal curve
Δ	54731953125 = 36 · 57 · 312	Discriminant
Eigenvalues	-2 3- 5- -2  1  0 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1767,26280]	[a1,a2,a3,a4,a6]
Generators	[-42:162:1] [8:-113:1]	Generators of the group modulo torsion
j	870928384/78125	j-invariant
L	5.0463592331191	L(r)(E,1)/r!
Ω	1.0900475740236	Real period
R	0.33067752227231	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4805d1 43245h1	Quadratic twists by: -3 -31

Hecke Eigenvalues for elliptic curve 43245n1

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	1	0	-2	-8	-4	-3	-	-8	3	-6	-2	-12	-5	-1	8	-15	-2	9	-4	-7	-12

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Quadratic twists for elliptic curve 43245n1

-3	-31
4805d1	43245h1

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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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