Cremona's table of elliptic curves

1738 = 2 · 11 · 79

Field	Data	Notes
Atkin-Lehner	2+ 11+ 79-	Signs for the Atkin-Lehner involutions
Class	1738a	Isogeny class
Conductor	1738	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	152944 = 24 · 112 · 79	Discriminant
Eigenvalues	2+ -1 -3 -3 11+ -3  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-14,4]	[a1,a2,a3,a4,a6]
Generators	[-4:6:1] [-3:7:1]	Generators of the group modulo torsion
j	338608873/152944	j-invariant
L	1.9397232981585	L(r)(E,1)/r!
Ω	2.9138506116732	Real period
R	0.16642267884189	Regulator
r	2	Rank of the group of rational points
S	0.99999999999975	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13904h1 55616p1 15642j1 43450o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1738a1

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	-3	-3	+	-3	0	-4	-8	-6	-8	-12	0	4	11	14	-3	-10	-2	-13	-6	-	6	5	1

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Quadratic twists for elliptic curve 1738a1

-4	8	-3	5	-7	-11
13904h1	55616p1	15642j1	43450o1	85162i1	19118f1

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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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