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	7616i	Isogeny class
Conductor	7616	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	3493855232 = 222 · 72 · 17	Discriminant
Eigenvalues	2-  0 -2 7+  0  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1196,-15664]	[a1,a2,a3,a4,a6]
Generators	[-20:16:1]	Generators of the group modulo torsion
j	721734273/13328	j-invariant
L	3.3532748640437	L(r)(E,1)/r!
Ω	0.81274383326212	Real period
R	2.062934670685	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	7616e1 1904c1 68544dl1 53312bs1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7616i1

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

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Quadratic twists for elliptic curve 7616i1

-4	8	-3	-7	17
7616e1	1904c1	68544dl1	53312bs1	129472cv1

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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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