Cremona's table of elliptic curves

1872 = 2⁴ · 3² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	1872n	Isogeny class
Conductor	1872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-4968677376 = -1 · 219 · 36 · 13	Discriminant
Eigenvalues	2- 3-  1 -1 -2 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-387,4482]	[a1,a2,a3,a4,a6]
Generators	[1:64:1]	Generators of the group modulo torsion
j	-2146689/1664	j-invariant
L	3.0181519491244	L(r)(E,1)/r!
Ω	1.2548007910185	Real period
R	0.60132093690238	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	234a1 7488bz1 208d1 46800dr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872n1

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	-2	+	3	-6	-4	-2	-4	3	0	5	13	-12	-10	-8	2	-5	-10	4	0	-6	14

---

Quadratic twists for elliptic curve 1872n1

-4	8	-3	5	-7	13
234a1	7488bz1	208d1	46800dr1	91728fk1	24336bl1

---

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