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	2604b	Isogeny class
Conductor	2604	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	15499008 = 28 · 32 · 7 · 312	Discriminant
Eigenvalues	2- 3-  0 7+  0  0 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-68,84]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1]	Generators of the group modulo torsion
j	137842000/60543	j-invariant
L	3.6971585079468	L(r)(E,1)/r!
Ω	1.9890652593379	Real period
R	1.8587416831047	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	10416bc2 41664a2 7812e2 65100f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2604b2

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	0	-2	-4	-8	-2	+	-2	0	-6	4	10	4	-4	-4	-6	8	14	-12	-14	2

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Quadratic twists for elliptic curve 2604b2

-4	8	-3	5	-7	-31
10416bc2	41664a2	7812e2	65100f2	18228f2	80724a2

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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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