Cremona's table of elliptic curves

3450 = 2 · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	3450w	Isogeny class
Conductor	3450	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-33120000000000 = -1 · 214 · 32 · 510 · 23	Discriminant
Eigenvalues	2- 3- 5+  2  6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,4287,-254583]	[a1,a2,a3,a4,a6]
j	557644990391/2119680000	j-invariant
L	4.6635248634131	L(r)(E,1)/r!
Ω	0.33310891881522	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27600bj1 110400bf1 10350k1 690a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450w1

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

---

Quadratic twists for elliptic curve 3450w1

-4	8	-3	5	-23
27600bj1	110400bf1	10350k1	690a1	79350di1

---

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