Cremona's table of elliptic curves

1696 = 2⁵ · 53

Field	Data	Notes
Atkin-Lehner	2- 53-	Signs for the Atkin-Lehner involutions
Class	1696f	Isogeny class
Conductor	1696	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-27136 = -1 · 29 · 53	Discriminant
Eigenvalues	2- -2  1 -2  3  0  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,-8]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-8/53	j-invariant
L	2.1621143163656	L(r)(E,1)/r!
Ω	1.7052071491361	Real period
R	0.63397409442629	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1696b1 3392b1 15264c1 42400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1696f1

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
-	-2	1	-2	3	0	3	-8	3	10	-7	-2	6	1	-12	-	-7	-6	12	4	-16	-17	2	-7	-13

---

Quadratic twists for elliptic curve 1696f1

-4	8	-3	5	-7	53
1696b1	3392b1	15264c1	42400a1	83104n1	89888d1

---

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