Cremona's table of elliptic curves

2604 = 2² · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 31-	Signs for the Atkin-Lehner involutions
Class	2604f	Isogeny class
Conductor	2604	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	1575555408 = 24 · 33 · 76 · 31	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-393,-2448]	[a1,a2,a3,a4,a6]
Generators	[-7:3:1]	Generators of the group modulo torsion
j	420616192000/98472213	j-invariant
L	3.7961522695263	L(r)(E,1)/r!
Ω	1.0901619911067	Real period
R	2.3214606639469	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	10416o1 41664x1 7812j1 65100c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2604f1

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
-	-	0	-	0	-4	-6	-4	0	-6	-	-10	0	2	0	6	0	8	-4	-6	-4	-10	12	6	2

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Quadratic twists for elliptic curve 2604f1

-4	8	-3	5	-7	-31
10416o1	41664x1	7812j1	65100c1	18228a1	80724i1

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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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