Cremona's table of elliptic curves

1314 = 2 · 3² · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 73-	Signs for the Atkin-Lehner involutions
Class	1314a	Isogeny class
Conductor	1314	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	10169927073792 = 218 · 312 · 73	Discriminant
Eigenvalues	2+ 3-  0  2  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8442,258228]	[a1,a2,a3,a4,a6]
Generators	[33:105:1]	Generators of the group modulo torsion
j	91276959390625/13950517248	j-invariant
L	2.0895657322661	L(r)(E,1)/r!
Ω	0.69347345131445	Real period
R	1.506593892171	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	10512s1 42048q1 438a1 32850bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1314a1

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	2	0	-4	-6	-4	0	0	2	2	-6	-4	6	12	0	-10	-4	-12	-	-4	0	-6	2

---

Quadratic twists for elliptic curve 1314a1

-4	8	-3	5	-7	73
10512s1	42048q1	438a1	32850bm1	64386o1	95922d1

---

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