Cremona's table of elliptic curves

7616 = 2⁶ · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	7616b	Isogeny class
Conductor	7616	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	873463808 = 220 · 72 · 17	Discriminant
Eigenvalues	2+ -2  0 7+  2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1153,-15393]	[a1,a2,a3,a4,a6]
Generators	[-19:4:1]	Generators of the group modulo torsion
j	647214625/3332	j-invariant
L	2.8122918298803	L(r)(E,1)/r!
Ω	0.81949334951999	Real period
R	1.7158722712805	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	7616k1 238d1 68544bi1 53312w1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7616b1

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

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Quadratic twists for elliptic curve 7616b1

-4	8	-3	-7	17
7616k1	238d1	68544bi1	53312w1	129472be1

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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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