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	1617h	Isogeny class
Conductor	1617	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-1178793 = -1 · 37 · 72 · 11	Discriminant
Eigenvalues	-1 3- -4 7- 11+  0  7  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,20,41]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	17999471/24057	j-invariant
L	1.7641331676507	L(r)(E,1)/r!
Ω	1.8460996989995	Real period
R	0.13651430856453	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	25872cc1 103488ce1 4851p1 40425i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617h1

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	-	-4	-	+	0	7	5	-9	1	-2	-3	2	-1	-7	0	-7	10	-12	-15	4	-8	-4	-12	1

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Quadratic twists for elliptic curve 1617h1

-4	8	-3	5	-7	-11
25872cc1	103488ce1	4851p1	40425i1	1617b1	17787q1

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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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