Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	50400br	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	45209390625000000 = 26 · 310 · 512 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1181325,494093500]	[a1,a2,a3,a4,a6]
Generators	[6035:461700:1]	Generators of the group modulo torsion
j	250094631024064/62015625	j-invariant
L	6.3448483524031	L(r)(E,1)/r!
Ω	0.35055543518273	Real period
R	4.5248537860429	Regulator
r	1	Rank of the group of rational points
S	0.99999999999763	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400de1 100800fk2 16800by1 10080bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400br1

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
+	-	+	-	-4	2	-2	8	0	2	0	6	-2	-4	8	-6	0	-2	-4	-4	2	4	-12	-18	-6

---

Quadratic twists for elliptic curve 50400br1

-4	8	-3	5
50400de1	100800fk2	16800by1	10080bn1

---

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