Cremona's table of elliptic curves

1218 = 2 · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 29-	Signs for the Atkin-Lehner involutions
Class	1218f	Isogeny class
Conductor	1218	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-4394621952 = -1 · 210 · 36 · 7 · 292	Discriminant
Eigenvalues	2- 3+  0 7+ -4 -4 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-203,-3463]	[a1,a2,a3,a4,a6]
Generators	[27:94:1]	Generators of the group modulo torsion
j	-925434168625/4394621952	j-invariant
L	3.1051991732222	L(r)(E,1)/r!
Ω	0.57236182184807	Real period
R	0.5425238118077	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	9744u1 38976m1 3654e1 30450bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1218f1

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	+	-4	-4	-4	8	-8	-	2	-6	0	-12	6	-6	6	6	8	-8	-12	8	-6	-8	-8

---

Quadratic twists for elliptic curve 1218f1

-4	8	-3	5	-7	29
9744u1	38976m1	3654e1	30450bj1	8526ba1	35322m1

---

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