Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	3136s	Isogeny class
Conductor	3136	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	107943428096 = 217 · 77	Discriminant
Eigenvalues	2-  0  2 7- -4  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-58604,5460560]	[a1,a2,a3,a4,a6]
Generators	[28:1960:1]	Generators of the group modulo torsion
j	1443468546/7	j-invariant
L	3.6145520979503	L(r)(E,1)/r!
Ω	0.93493147424957	Real period
R	1.9330572333398	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	3136e3 784c4 28224gd4 78400gz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136s4

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	-	-4	2	6	-8	0	-6	8	2	-2	-4	-8	-6	0	-6	-4	8	-10	-16	-8	6	6

---

Quadratic twists for elliptic curve 3136s4

-4	8	-3	5	-7
3136e3	784c4	28224gd4	78400gz4	448b3

---

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