Cremona's table of elliptic curves

784 = 2⁴ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7+	Signs for the Atkin-Lehner involutions
Class	784g	Isogeny class
Conductor	784	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	92236816 = 24 · 78	Discriminant
Eigenvalues	2- -1  3 7+  3  2  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-114,127]	[a1,a2,a3,a4,a6]
j	1792	j-invariant
L	1.6482722735833	L(r)(E,1)/r!
Ω	1.6482722735833	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	196b1 3136o1 7056bo1 19600bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 784g1

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
-	-1	3	+	3	2	3	1	-3	-6	7	-1	6	4	9	3	-9	-1	7	0	-1	13	-12	15	-10

---

Quadratic twists for elliptic curve 784g1

-4	8	-3	5	-7	-11
196b1	3136o1	7056bo1	19600bs1	784i1	94864bi1

---

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