Cremona's table of elliptic curves

15675 = 3 · 5² · 11 · 19

Field	Data	Notes
Atkin-Lehner	3- 5- 11- 19-	Signs for the Atkin-Lehner involutions
Class	15675bb	Isogeny class
Conductor	15675	Conductor
∏ cp	495	Product of Tamagawa factors cp
deg	166320	Modular degree for the optimal curve
Δ	364888250759401875 = 311 · 54 · 113 · 195	Discriminant
Eigenvalues	-1 3- 5-  1 11- -3 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-190038,13103217]	[a1,a2,a3,a4,a6]
Generators	[57:1539:1]	Generators of the group modulo torsion
j	1214409598355165425/583821201215043	j-invariant
L	3.8218821919986	L(r)(E,1)/r!
Ω	0.2689581780103	Real period
R	0.028706969174047	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	47025bk1 15675l1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 15675bb1

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	-	-	1	-	-3	-3	-	7	4	-3	4	-12	-5	-8	14	6	-4	4	10	-16	-4	-12	-6	-12

---

Quadratic twists for elliptic curve 15675bb1

-3	5
47025bk1	15675l1

---

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