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	6300z	Isogeny class
Conductor	6300	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	71442000 = 24 · 36 · 53 · 72	Discriminant
Eigenvalues	2- 3- 5- 7-  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-720,7425]	[a1,a2,a3,a4,a6]
Generators	[10:35:1]	Generators of the group modulo torsion
j	28311552/49	j-invariant
L	4.2573454212861	L(r)(E,1)/r!
Ω	1.9460811043	Real period
R	0.36460842698001	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200ev1 100800hk1 700h1 6300s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300z1

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

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Quadratic twists for elliptic curve 6300z1

-4	8	-3	5	-7
25200ev1	100800hk1	700h1	6300s1	44100cx1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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