Cremona's table of elliptic curves

1705 = 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	5+ 11+ 31-	Signs for the Atkin-Lehner involutions
Class	1705a	Isogeny class
Conductor	1705	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	-36630859375 = -1 · 510 · 112 · 31	Discriminant
Eigenvalues	1 -2 5+  4 11+ -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-964,14661]	[a1,a2,a3,a4,a6]
j	-98925223576249/36630859375	j-invariant
L	1.0884008084022	L(r)(E,1)/r!
Ω	1.0884008084022	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27280n1 109120r1 15345l1 8525a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1705a1

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	-2	+	4	+	-4	4	-4	-2	2	-	-4	2	2	4	4	-12	10	12	8	8	16	10	6	6

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Quadratic twists for elliptic curve 1705a1

-4	8	-3	5	-7	-11	-31
27280n1	109120r1	15345l1	8525a1	83545f1	18755c1	52855d1

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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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