Cremona's table of elliptic curves

4272 = 2⁴ · 3 · 89

Field	Data	Notes
Atkin-Lehner	2+ 3+ 89-	Signs for the Atkin-Lehner involutions
Class	4272a	Isogeny class
Conductor	4272	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	1845504 = 28 · 34 · 89	Discriminant
Eigenvalues	2+ 3+ -2 -4  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2404,-44576]	[a1,a2,a3,a4,a6]
j	6004374601552/7209	j-invariant
L	0.68179045459362	L(r)(E,1)/r!
Ω	0.68179045459362	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	2136a1 17088m1 12816a1 106800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4272a1

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	-4	4	2	2	-4	-4	-6	-4	2	2	-4	0	6	-4	2	-4	-8	-6	0	4	-	18

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Quadratic twists for elliptic curve 4272a1

-4	8	-3	5
2136a1	17088m1	12816a1	106800s1

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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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