Cremona's table of elliptic curves

13300 = 2² · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 19-	Signs for the Atkin-Lehner involutions
Class	13300x	Isogeny class
Conductor	13300	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	22809500000000 = 28 · 59 · 74 · 19	Discriminant
Eigenvalues	2-  2 5- 7- -4  6  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14708,-642088]	[a1,a2,a3,a4,a6]
Generators	[-12162:14291:216]	Generators of the group modulo torsion
j	703791632/45619	j-invariant
L	6.8597450089964	L(r)(E,1)/r!
Ω	0.43528292801785	Real period
R	7.8796393879191	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	53200dh2 119700ck2 13300s2 93100br2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300x2

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	6	0	-	-4	-6	-8	6	-6	0	-8	2	-4	-2	10	-16	0	0	12	-14	-6

---

Quadratic twists for elliptic curve 13300x2

-4	-3	5	-7
53200dh2	119700ck2	13300s2	93100br2

---

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