Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	3136h	Isogeny class
Conductor	3136	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	-165288374272 = -1 · 212 · 79	Discriminant
Eigenvalues	2+  2  2 7- -4  6  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-457,-19767]	[a1,a2,a3,a4,a6]
j	-64	j-invariant
L	3.5010678785742	L(r)(E,1)/r!
Ω	0.43763348482177	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3136l1 1568f1 28224cj1 78400da1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136h1

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	6	4	6	-4	6	4	6	-4	-12	12	-6	6	-6	-12	8	0	0	6	16	12

---

Quadratic twists for elliptic curve 3136h1

-4	8	-3	5	-7
3136l1	1568f1	28224cj1	78400da1	3136m1

---

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