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	3450a	Isogeny class
Conductor	3450	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-4959375000000 = -1 · 26 · 3 · 511 · 232	Discriminant
Eigenvalues	2+ 3+ 5+  0  2  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,3350,-75500]	[a1,a2,a3,a4,a6]
Generators	[380:7310:1]	Generators of the group modulo torsion
j	265971760991/317400000	j-invariant
L	2.2404328742487	L(r)(E,1)/r!
Ω	0.41263296025711	Real period
R	1.357400577533	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	27600cu1 110400cu1 10350bo1 690i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450a1

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	2	0	-6	4	+	0	-8	6	-2	2	-4	2	0	-2	2	-10	10	0	4	4	-16

---

Quadratic twists for elliptic curve 3450a1

-4	8	-3	5	-23
27600cu1	110400cu1	10350bo1	690i1	79350c1

---

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