Cremona's table of elliptic curves

21450 = 2 · 3 · 5² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 11- 13+	Signs for the Atkin-Lehner involutions
Class	21450r	Isogeny class
Conductor	21450	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	3480000	Modular degree for the optimal curve
Δ	-3533056312500000 = -1 · 25 · 33 · 59 · 115 · 13	Discriminant
Eigenvalues	2+ 3+ 5- -3 11- 13+  2  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-325320075,-2258605987875]	[a1,a2,a3,a4,a6]
Generators	[168959754395:65880169486740:1092727]	Generators of the group modulo torsion
j	-1949513587550201844335429/1808924832	j-invariant
L	2.8424164934227	L(r)(E,1)/r!
Ω	0.017774272859596	Real period
R	15.991745574493	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	64350ex1 21450cx1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 21450r1

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
+	+	-	-3	-	+	2	5	6	0	-3	2	-8	11	-3	-14	5	-3	-13	12	-14	-5	-9	15	7

---

Quadratic twists for elliptic curve 21450r1

-3	5
64350ex1	21450cx1

---

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