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	1734b	Isogeny class
Conductor	1734	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	19144761127488 = 26 · 36 · 177	Discriminant
Eigenvalues	2+ 3+  0 -2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-73845,7690221]	[a1,a2,a3,a4,a6]
Generators	[-135:3969:1]	Generators of the group modulo torsion
j	1845026709625/793152	j-invariant
L	1.8045805560692	L(r)(E,1)/r!
Ω	0.6757200123787	Real period
R	1.3353019912172	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	13872be1 55488bc1 5202h1 43350cy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1734b1

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	0	2	+	-4	6	0	10	-8	-6	-4	12	6	-12	-8	-4	-6	-2	10	12	-18	-14

---

Quadratic twists for elliptic curve 1734b1

-4	8	-3	5	-7	17
13872be1	55488bc1	5202h1	43350cy1	84966bs1	102c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations