Cremona's table of elliptic curves

13650 = 2 · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	13650bw	Isogeny class
Conductor	13650	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	9828000000 = 28 · 33 · 56 · 7 · 13	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1413,-20469]	[a1,a2,a3,a4,a6]
Generators	[-21:32:1]	Generators of the group modulo torsion
j	19968681097/628992	j-invariant
L	6.0090755565915	L(r)(E,1)/r!
Ω	0.78018945516742	Real period
R	1.9255180638471	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	109200fe1 40950bl1 546c1 95550kb1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650bw1

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
-	+	+	-	-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 13650bw1

-4	-3	5	-7
109200fe1	40950bl1	546c1	95550kb1

---

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