Cremona's table of elliptic curves

2618 = 2 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 7+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	2618b	Isogeny class
Conductor	2618	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-20944 = -1 · 24 · 7 · 11 · 17	Discriminant
Eigenvalues	2+  0  3 7+ 11- -3 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,7,-3]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	34965783/20944	j-invariant
L	2.6993762329011	L(r)(E,1)/r!
Ω	2.2337779948988	Real period
R	0.60421766152804	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	20944j1 83776d1 23562ba1 65450bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2618b1

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	3	+	-	-3	-	-4	-1	-1	10	-8	-8	-1	-4	-5	-15	4	4	-3	-6	-2	-14	6	18

---

Quadratic twists for elliptic curve 2618b1

-4	8	-3	5	-7	-11	17
20944j1	83776d1	23562ba1	65450bd1	18326n1	28798x1	44506g1

---

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