Cremona's table of elliptic curves

1617 = 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1617a	Isogeny class
Conductor	1617	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-79233 = -1 · 3 · 74 · 11	Discriminant
Eigenvalues	1 3+  0 7+ 11+  4  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-25,-62]	[a1,a2,a3,a4,a6]
Generators	[6:4:1]	Generators of the group modulo torsion
j	-765625/33	j-invariant
L	2.9836426537259	L(r)(E,1)/r!
Ω	1.0593809327073	Real period
R	0.9388006906074	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	25872cg1 103488cm1 4851h1 40425bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617a1

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	+	0	+	+	4	3	1	-1	-5	-10	-11	10	-3	-9	-8	-9	-2	4	-7	4	-8	8	0	-1

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Quadratic twists for elliptic curve 1617a1

-4	8	-3	5	-7	-11
25872cg1	103488cm1	4851h1	40425bt1	1617e1	17787b1

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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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