Cremona's table of elliptic curves

6512 = 2⁴ · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 11+ 37+	Signs for the Atkin-Lehner involutions
Class	6512b	Isogeny class
Conductor	6512	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	71632 = 24 · 112 · 37	Discriminant
Eigenvalues	2-  0 -2  0 11+  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16,-21]	[a1,a2,a3,a4,a6]
j	28311552/4477	j-invariant
L	1.2062810556982	L(r)(E,1)/r!
Ω	2.4125621113965	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	1628a1 26048m1 58608bj1 71632j1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6512b1

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	+	4	4	4	-6	-8	2	+	-6	8	4	-2	14	-4	-4	0	2	12	-4	2	-10

---

Quadratic twists for elliptic curve 6512b1

-4	8	-3	-11
1628a1	26048m1	58608bj1	71632j1

---

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