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	4275l	Isogeny class
Conductor	4275	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-4996098984375 = -1 · 311 · 57 · 192	Discriminant
Eigenvalues	-1 3- 5+  2  6  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,4270,4272]	[a1,a2,a3,a4,a6]
Generators	[18:285:1]	Generators of the group modulo torsion
j	756058031/438615	j-invariant
L	2.6296561156747	L(r)(E,1)/r!
Ω	0.46164125431049	Real period
R	2.8481597897943	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68400ep1 1425c1 855c1 81225bb1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 4275l1

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	6	0	-6	-	-8	-4	0	-4	0	2	-8	2	-12	2	8	-16	-14	8	0	0	12

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Quadratic twists for elliptic curve 4275l1

-4	-3	5	-19
68400ep1	1425c1	855c1	81225bb1

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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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