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	1224d	Isogeny class
Conductor	1224	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	431474688 = 211 · 36 · 172	Discriminant
Eigenvalues	2+ 3-  0  0 -2 -6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-435,-3346]	[a1,a2,a3,a4,a6]
Generators	[-10:2:1]	Generators of the group modulo torsion
j	6097250/289	j-invariant
L	2.5787402992546	L(r)(E,1)/r!
Ω	1.0484582846976	Real period
R	2.459554506738	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	2448f2 9792o2 136b2 30600bx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1224d2

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	0	-2	-6	-	4	-4	0	-8	-4	-6	8	8	-10	0	12	8	-12	2	-4	-16	-10	-18

---

Quadratic twists for elliptic curve 1224d2

-4	8	-3	5	-7	17
2448f2	9792o2	136b2	30600bx2	59976j2	20808h2

---

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