Cremona's table of elliptic curves

6300 = 2² · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	6300g	Isogeny class
Conductor	6300	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	-28481916093750000 = -1 · 24 · 312 · 510 · 73	Discriminant
Eigenvalues	2- 3- 5+ 7+  3  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-148125,-23396875]	[a1,a2,a3,a4,a6]
Generators	[1069:32247:1]	Generators of the group modulo torsion
j	-3155449600/250047	j-invariant
L	4.0734001396715	L(r)(E,1)/r!
Ω	0.12112784353151	Real period
R	5.6048221737058	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	25200ep1 100800dv1 2100a1 6300bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300g1

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	4	-6	-4	3	-3	-10	7	0	1	-12	6	-12	-4	7	-9	-2	17	-6	0	-2

---

Quadratic twists for elliptic curve 6300g1

-4	8	-3	5	-7
25200ep1	100800dv1	2100a1	6300bb1	44100cb1

---

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