Cremona's table of elliptic curves

7216 = 2⁴ · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 11- 41+	Signs for the Atkin-Lehner involutions
Class	7216g	Isogeny class
Conductor	7216	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	-75739136 = -1 · 212 · 11 · 412	Discriminant
Eigenvalues	2- -1 -3 -4 11- -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,43,-419]	[a1,a2,a3,a4,a6]
Generators	[12:41:1]	Generators of the group modulo torsion
j	2097152/18491	j-invariant
L	1.8861713276067	L(r)(E,1)/r!
Ω	0.95854591123761	Real period
R	0.98387114560395	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	451a1 28864m1 64944bi1 79376s1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7216g1

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	-4	-	-6	2	8	5	-8	-3	7	+	-6	0	-2	-9	12	9	13	6	-10	12	13	-5

---

Quadratic twists for elliptic curve 7216g1

-4	8	-3	-11
451a1	28864m1	64944bi1	79376s1

---

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