Cremona's table of elliptic curves

1534 = 2 · 13 · 59

Field	Data	Notes
Atkin-Lehner	2+ 13- 59+	Signs for the Atkin-Lehner involutions
Class	1534b	Isogeny class
Conductor	1534	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-638144 = -1 · 26 · 132 · 59	Discriminant
Eigenvalues	2+ -3 -1 -5  0 13- -6 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,5,37]	[a1,a2,a3,a4,a6]
Generators	[-2:5:1] [1:6:1]	Generators of the group modulo torsion
j	12326391/638144	j-invariant
L	1.5675216281173	L(r)(E,1)/r!
Ω	2.1907848693674	Real period
R	0.17887671788761	Regulator
r	2	Rank of the group of rational points
S	0.99999999999761	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12272i1 49088f1 13806j1 38350t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1534b1

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
+	-3	-1	-5	0	-	-6	-5	-6	-5	-8	-4	5	-2	2	-11	+	-6	-2	-16	-2	-9	16	18	12

---

Quadratic twists for elliptic curve 1534b1

-4	8	-3	5	-7	13	-59
12272i1	49088f1	13806j1	38350t1	75166f1	19942l1	90506e1

---

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