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	1617i	Isogeny class
Conductor	1617	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-1440747 = -1 · 35 · 72 · 112	Discriminant
Eigenvalues	-2 3-  0 7- 11+  5 -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,12,-52]	[a1,a2,a3,a4,a6]
Generators	[6:16:1]	Generators of the group modulo torsion
j	3584000/29403	j-invariant
L	1.801241745902	L(r)(E,1)/r!
Ω	1.3360454989478	Real period
R	0.1348188925692	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	25872bv1 103488bs1 4851t1 40425r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617i1

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	-	+	5	-6	-7	-4	-2	7	7	-4	-9	-6	-2	-12	2	7	8	5	-11	4	-6	-2

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Quadratic twists for elliptic curve 1617i1

-4	8	-3	5	-7	-11
25872bv1	103488bs1	4851t1	40425r1	1617c1	17787w1

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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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