Cremona's table of elliptic curves

6248 = 2³ · 11 · 71

Field	Data	Notes
Atkin-Lehner	2+ 11+ 71+	Signs for the Atkin-Lehner involutions
Class	6248a	Isogeny class
Conductor	6248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2976	Modular degree for the optimal curve
Δ	1007877376 = 28 · 11 · 713	Discriminant
Eigenvalues	2+  0  3  1 11+ -3 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1516,-22668]	[a1,a2,a3,a4,a6]
Generators	[-22:6:1]	Generators of the group modulo torsion
j	1505155433472/3937021	j-invariant
L	4.6350429835815	L(r)(E,1)/r!
Ω	0.76523182995844	Real period
R	1.5142610389825	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	12496b1 49984g1 56232o1 68728e1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6248a1

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	3	1	+	-3	-3	-2	4	4	-10	5	-5	6	-2	-4	8	7	-8	+	4	-10	-2	-15	2

---

Quadratic twists for elliptic curve 6248a1

-4	8	-3	-11
12496b1	49984g1	56232o1	68728e1

---

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