Cremona's table of elliptic curves

4275 = 3² · 5² · 19

Field	Data	Notes
Atkin-Lehner	3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	4275f	Isogeny class
Conductor	4275	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-1542005859375 = -1 · 37 · 59 · 192	Discriminant
Eigenvalues	1 3- 5+  2  2  4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,333,59616]	[a1,a2,a3,a4,a6]
j	357911/135375	j-invariant
L	2.6310938677301	L(r)(E,1)/r!
Ω	0.65777346693252	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	68400fl1 1425g1 855b1 81225bf1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4275f1

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	2	4	2	+	-4	-4	0	0	0	10	12	-2	-4	2	16	0	2	-8	-12	0	16

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Quadratic twists for elliptic curve 4275f1

-4	-3	5	-19
68400fl1	1425g1	855b1	81225bf1

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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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