Cremona's table of elliptic curves

1729 = 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	7+ 13+ 19-	Signs for the Atkin-Lehner involutions
Class	1729a	Isogeny class
Conductor	1729	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-624169 = -1 · 7 · 13 · 193	Discriminant
Eigenvalues	1  0  3 7+  3 13+  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-68,-203]	[a1,a2,a3,a4,a6]
j	-35062107417/624169	j-invariant
L	2.4894642183498	L(r)(E,1)/r!
Ω	0.82982140611659	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27664o1 110656f1 15561e1 43225d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1729a1

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	3	+	3	+	4	-	6	4	3	5	12	8	-8	-12	-1	-4	-12	10	2	9	-6	-12	-2

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Quadratic twists for elliptic curve 1729a1

-4	8	-3	5	-7	13	-19
27664o1	110656f1	15561e1	43225d1	12103b1	22477h1	32851h1

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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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