Cremona's table of elliptic curves

8464 = 2⁴ · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	8464a	Isogeny class
Conductor	8464	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12672	Modular degree for the optimal curve
Δ	-3486541257728 = -1 · 210 · 237	Discriminant
Eigenvalues	2+  0  0  4  6 -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2645,73002]	[a1,a2,a3,a4,a6]
j	13500/23	j-invariant
L	2.1668397477133	L(r)(E,1)/r!
Ω	0.54170993692833	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	4232a1 33856x1 76176c1 368a1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 8464a1

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	0	4	6	-2	-6	-6	-	-6	0	8	6	-2	8	8	-4	4	2	8	6	12	10	-10	18

---

Quadratic twists for elliptic curve 8464a1

-4	8	-3	-23
4232a1	33856x1	76176c1	368a1

---

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