Cremona's table of elliptic curves

496 = 2⁴ · 31

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	496f	Isogeny class
Conductor	496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-2031616 = -1 · 216 · 31	Discriminant
Eigenvalues	2-  0 -2  0  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11,-70]	[a1,a2,a3,a4,a6]
Generators	[7:14:1]	Generators of the group modulo torsion
j	-35937/496	j-invariant
L	1.7961902527622	L(r)(E,1)/r!
Ω	1.1195541660226	Real period
R	1.604379946299	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	62a1 1984j1 4464x1 12400r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 496f1

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

---

Quadratic twists for elliptic curve 496f1

-4	8	-3	5	-7	-11	13	-31
62a1	1984j1	4464x1	12400r1	24304n1	60016n1	83824k1	15376u1

---

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