Cremona's table of elliptic curves

10650 = 2 · 3 · 5² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 71-	Signs for the Atkin-Lehner involutions
Class	10650f	Isogeny class
Conductor	10650	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	7066828800000000 = 220 · 35 · 58 · 71	Discriminant
Eigenvalues	2+ 3+ 5-  2 -3  6 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2090700,1162674000]	[a1,a2,a3,a4,a6]
Generators	[824:100:1]	Generators of the group modulo torsion
j	2587254552097843945/18091081728	j-invariant
L	3.1205971994665	L(r)(E,1)/r!
Ω	0.37523763974572	Real period
R	1.3860537380974	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	85200dr2 31950cq2 10650bg1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 10650f2

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	6	-3	5	1	10	-8	-3	-3	-9	-8	-9	-15	12	2	-	1	-5	-4	0	2

---

Quadratic twists for elliptic curve 10650f2

-4	-3	5
85200dr2	31950cq2	10650bg1

---

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