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	3450j	Isogeny class
Conductor	3450	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	555323040000000000 = 214 · 38 · 510 · 232	Discriminant
Eigenvalues	2+ 3- 5+  0  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2160276,-1221768302]	[a1,a2,a3,a4,a6]
Generators	[-838:906:1]	Generators of the group modulo torsion
j	71356102305927901489/35540674560000	j-invariant
L	3.0162633344312	L(r)(E,1)/r!
Ω	0.12453322966984	Real period
R	3.0275687686208	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	27600bg2 110400w2 10350bh2 690g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450j2

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	0	-6	-2	0	-	6	8	-10	-6	8	-8	6	-4	-6	-8	-8	-10	-8	8	-6	-18

---

Quadratic twists for elliptic curve 3450j2

-4	8	-3	5	-23
27600bg2	110400w2	10350bh2	690g2	79350bb2

---

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