Cremona's table of elliptic curves

1248 = 2⁵ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	1248j	Isogeny class
Conductor	1248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	7488 = 26 · 32 · 13	Discriminant
Eigenvalues	2- 3-  0  2  0 13-  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18,-36]	[a1,a2,a3,a4,a6]
j	10648000/117	j-invariant
L	2.308753302428	L(r)(E,1)/r!
Ω	2.308753302428	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1248g1 2496q2 3744e1 31200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248j1

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
-	-	0	2	0	-	2	-2	8	6	2	-6	0	4	8	-6	4	2	2	4	-2	12	-12	12	-18

---

Quadratic twists for elliptic curve 1248j1

-4	8	-3	5	-7	13
1248g1	2496q2	3744e1	31200a1	61152bc1	16224i1

---

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