Cremona's table of elliptic curves

616 = 2³ · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	616d	Isogeny class
Conductor	616	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-16696064 = -1 · 28 · 72 · 113	Discriminant
Eigenvalues	2+ -1 -1 7- 11-  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1,197]	[a1,a2,a3,a4,a6]
Generators	[29:154:1]	Generators of the group modulo torsion
j	-1024/65219	j-invariant
L	1.7957577414006	L(r)(E,1)/r!
Ω	1.7515268442222	Real period
R	0.042718865241401	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1232a1 4928k1 5544s1 15400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 616d1

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	-1	-	-	0	-2	-2	-7	-10	7	-9	-2	-4	8	2	-15	-14	3	3	10	10	0	-11	7

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Quadratic twists for elliptic curve 616d1

-4	8	-3	5	-7	-11	13
1232a1	4928k1	5544s1	15400o1	4312g1	6776e1	104104o1

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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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