Cremona's table of elliptic curves

2450 = 2 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	2450b	Isogeny class
Conductor	2450	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-9378906250 = -1 · 2 · 59 · 74	Discriminant
Eigenvalues	2+  2 5+ 7+  3 -5 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-12275,-528625]	[a1,a2,a3,a4,a6]
Generators	[505:10810:1]	Generators of the group modulo torsion
j	-5452947409/250	j-invariant
L	3.2003822560958	L(r)(E,1)/r!
Ω	0.2267818963084	Real period
R	3.5280398349607	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19600bx2 78400n2 22050du2 490e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2450b2

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	+	+	3	-5	-6	-1	-3	-6	-4	-11	3	10	-3	-3	0	-4	4	12	4	-10	12	6	-14

---

Quadratic twists for elliptic curve 2450b2

-4	8	-3	5	-7
19600bx2	78400n2	22050du2	490e2	2450h2

---

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