Cremona's table of elliptic curves

1736 = 2³ · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 31+	Signs for the Atkin-Lehner involutions
Class	1736c	Isogeny class
Conductor	1736	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-388864 = -1 · 28 · 72 · 31	Discriminant
Eigenvalues	2-  0  2 7- -6  0  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1,-30]	[a1,a2,a3,a4,a6]
Generators	[5:10:1]	Generators of the group modulo torsion
j	432/1519	j-invariant
L	3.0768787486769	L(r)(E,1)/r!
Ω	1.3923848159262	Real period
R	1.1048952536265	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3472a1 13888h1 15624n1 43400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1736c1

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	2	-	-6	0	4	-4	-6	-6	+	-6	2	-2	0	-2	12	0	-8	8	12	-14	-4	4	-2

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Quadratic twists for elliptic curve 1736c1

-4	8	-3	5	-7	-31
3472a1	13888h1	15624n1	43400b1	12152f1	53816e1

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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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