Cremona's table of elliptic curves

828 = 2² · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23+	Signs for the Atkin-Lehner involutions
Class	828a	Isogeny class
Conductor	828	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	9936 = 24 · 33 · 23	Discriminant
Eigenvalues	2- 3+  2  2  4 -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24,45]	[a1,a2,a3,a4,a6]
j	3538944/23	j-invariant
L	2.0500973964435	L(r)(E,1)/r!
Ω	4.100194792887	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	3312k1 13248a1 828b1 20700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 828a1

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
-	+	2	2	4	-2	2	-2	+	4	0	2	0	-2	12	-2	12	-14	2	0	6	6	4	-18	6

---

Quadratic twists for elliptic curve 828a1

-4	8	-3	5	-7	-11	-23
3312k1	13248a1	828b1	20700d1	40572d1	100188d1	19044e1

---

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