Cremona's table of elliptic curves

3400 = 2³ · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	3400f	Isogeny class
Conductor	3400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-19652000000000 = -1 · 211 · 59 · 173	Discriminant
Eigenvalues	2+ -1 5- -4  2 -5 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13208,-617588]	[a1,a2,a3,a4,a6]
j	-63710026/4913	j-invariant
L	0.44337333928123	L(r)(E,1)/r!
Ω	0.22168666964061	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6800f1 27200be1 30600cx1 3400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3400f1

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
+	-1	-	-4	2	-5	+	-7	-8	5	3	4	-4	0	3	-7	-3	11	-10	-1	11	-8	8	-9	1

---

Quadratic twists for elliptic curve 3400f1

-4	8	-3	5	17
6800f1	27200be1	30600cx1	3400g1	57800n1

---

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