Cremona's table of elliptic curves

1224 = 2³ · 3² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17+	Signs for the Atkin-Lehner involutions
Class	1224c	Isogeny class
Conductor	1224	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	17474724864 = 210 · 310 · 172	Discriminant
Eigenvalues	2+ 3- -2 -4 -4  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-651,-650]	[a1,a2,a3,a4,a6]
j	40873252/23409	j-invariant
L	1.0249644848853	L(r)(E,1)/r!
Ω	1.0249644848853	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2448d2 9792j2 408b2 30600co2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1224c2

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
+	-	-2	-4	-4	6	+	4	4	6	-4	10	6	4	8	-6	4	-14	-12	12	10	-4	-4	6	-6

---

Quadratic twists for elliptic curve 1224c2

-4	8	-3	5	-7	17
2448d2	9792j2	408b2	30600co2	59976r2	20808k2

---

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