Cremona's table of elliptic curves

7800 = 2³ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	7800s	Isogeny class
Conductor	7800	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	49280	Modular degree for the optimal curve
Δ	-1151455500000000 = -1 · 28 · 311 · 59 · 13	Discriminant
Eigenvalues	2- 3+ 5- -1  3 13-  7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-152833,23106037]	[a1,a2,a3,a4,a6]
j	-789601498112/2302911	j-invariant
L	1.9591454177006	L(r)(E,1)/r!
Ω	0.48978635442516	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15600x1 62400dj1 23400v1 7800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7800s1

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
-	+	-	-1	3	-	7	0	7	-4	8	5	-3	8	-6	11	-4	1	-12	-9	-6	-13	2	3	19

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Quadratic twists for elliptic curve 7800s1

-4	8	-3	5	13
15600x1	62400dj1	23400v1	7800j1	101400t1

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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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