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	50400bh	Isogeny class
Conductor	50400	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-102876480000000 = -1 · 212 · 38 · 57 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7-  2  0 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-300,-488000]	[a1,a2,a3,a4,a6]
Generators	[110:900:1]	Generators of the group modulo torsion
j	-64/2205	j-invariant
L	6.8665910181719	L(r)(E,1)/r!
Ω	0.27235518927521	Real period
R	0.78787178570066	Regulator
r	1	Rank of the group of rational points
S	0.99999999999428	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400x2 100800nj1 16800bv2 10080bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bh2

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	0	-6	6	8	-6	6	10	-2	-4	-8	-12	12	-10	-4	-2	-4	-4	-12	-6	-16

---

Quadratic twists for elliptic curve 50400bh2

-4	8	-3	5
50400x2	100800nj1	16800bv2	10080bv2

---

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