Cremona's table of elliptic curves

618 = 2 · 3 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3- 103-	Signs for the Atkin-Lehner involutions
Class	618d	Isogeny class
Conductor	618	Conductor
∏ cp	30	Product of Tamagawa factors cp
Δ	-1087621779456 = -1 · 212 · 35 · 1033	Discriminant
Eigenvalues	2+ 3- -3  2 -6 -1  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-20330,-1118500]	[a1,a2,a3,a4,a6]
Generators	[477:-10127:1]	Generators of the group modulo torsion
j	-929191309825663513/1087621779456	j-invariant
L	1.6716285286318	L(r)(E,1)/r!
Ω	0.1998974690207	Real period
R	0.27874765612278	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	4944f2 19776h2 1854i2 15450u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 618d2

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
+	-	-3	2	-6	-1	0	-4	3	-6	-7	-10	0	5	6	6	3	-1	-13	-12	-16	14	-9	6	17

---

Quadratic twists for elliptic curve 618d2

-4	8	-3	5	-7	-11	13	-103
4944f2	19776h2	1854i2	15450u2	30282f2	74778br2	104442bl2	63654b2

---

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