Cremona's table of elliptic curves

1850 = 2 · 5² · 37

Field	Data	Notes
Atkin-Lehner	2+ 5- 37-	Signs for the Atkin-Lehner involutions
Class	1850f	Isogeny class
Conductor	1850	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	1212416000 = 218 · 53 · 37	Discriminant
Eigenvalues	2+  0 5-  2  0 -2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-857,-9299]	[a1,a2,a3,a4,a6]
Generators	[-15:11:1]	Generators of the group modulo torsion
j	557238592989/9699328	j-invariant
L	2.2592462496032	L(r)(E,1)/r!
Ω	0.88326137766168	Real period
R	2.5578456238903	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	14800bh1 59200bm1 16650cr1 1850o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1850f1

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	-2	6	-6	-4	0	-4	-	-10	4	2	-2	-6	0	-8	0	-8	4	12	6	10

---

Quadratic twists for elliptic curve 1850f1

-4	8	-3	5	-7	37
14800bh1	59200bm1	16650cr1	1850o1	90650bh1	68450bi1

---

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