Cremona's table of elliptic curves

13104 = 2⁴ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	13104ck	Isogeny class
Conductor	13104	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	1878160048128 = 220 · 39 · 7 · 13	Discriminant
Eigenvalues	2- 3-  2 7- -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8139,-274822]	[a1,a2,a3,a4,a6]
Generators	[-2876:855:64]	Generators of the group modulo torsion
j	19968681097/628992	j-invariant
L	5.5397311856249	L(r)(E,1)/r!
Ω	0.50361012779168	Real period
R	5.5000196381242	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	1638q1 52416ga1 4368t1 91728el1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104ck1

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

---

Quadratic twists for elliptic curve 13104ck1

-4	8	-3	-7
1638q1	52416ga1	4368t1	91728el1

---

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