Cremona's table of elliptic curves

1615 = 5 · 17 · 19

Field	Data	Notes
Atkin-Lehner	5- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	1615a	Isogeny class
Conductor	1615	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	3835625 = 54 · 17 · 192	Discriminant
Eigenvalues	-1 -2 5- -4 -4 -6 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-215,1192]	[a1,a2,a3,a4,a6]
Generators	[-17:11:1] [-11:53:1]	Generators of the group modulo torsion
j	1099424306161/3835625	j-invariant
L	1.7043207462393	L(r)(E,1)/r!
Ω	2.4934265787949	Real period
R	0.3417627695026	Regulator
r	2	Rank of the group of rational points
S	0.9999999999992	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25840bb1 103360j1 14535j1 8075c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1615a1

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

---

Quadratic twists for elliptic curve 1615a1

-4	8	-3	5	-7	17	-19
25840bb1	103360j1	14535j1	8075c1	79135p1	27455a1	30685g1

---

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