Cremona's table of elliptic curves

7056 = 2⁴ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	7056r	Isogeny class
Conductor	7056	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-576108288 = -1 · 28 · 38 · 73	Discriminant
Eigenvalues	2+ 3-  0 7-  0 -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,105,1078]	[a1,a2,a3,a4,a6]
Generators	[2:36:1]	Generators of the group modulo torsion
j	2000/9	j-invariant
L	4.0684536106242	L(r)(E,1)/r!
Ω	1.1712787239902	Real period
R	1.7367572411646	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	3528i1 28224fa1 2352g1 7056q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7056r1

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	-	0	-4	4	-4	4	-2	8	-6	12	-4	8	-6	-12	-4	4	-12	-8	16	4	4	-16

---

Quadratic twists for elliptic curve 7056r1

-4	8	-3	-7
3528i1	28224fa1	2352g1	7056q1

---

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