Cremona's table of elliptic curves

1734 = 2 · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	1734a	Isogeny class
Conductor	1734	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-499392 = -1 · 26 · 33 · 172	Discriminant
Eigenvalues	2+ 3+  0  1  0 -1 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,20,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	2828375/1728	j-invariant
L	1.9267049253424	L(r)(E,1)/r!
Ω	1.8123438362918	Real period
R	0.5315506050123	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	13872bd1 55488y1 5202g1 43350cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734a1

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	1	0	-1	+	-7	6	0	-5	-5	12	11	-6	-12	6	-5	-7	12	-2	-8	-6	0	7

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Quadratic twists for elliptic curve 1734a1

-4	8	-3	5	-7	17
13872bd1	55488y1	5202g1	43350cv1	84966br1	1734h1

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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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