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	7800q	Isogeny class
Conductor	7800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-1579500000000 = -1 · 28 · 35 · 59 · 13	Discriminant
Eigenvalues	2- 3+ 5+  3 -3 13-  1 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2633,80637]	[a1,a2,a3,a4,a6]
Generators	[7:250:1]	Generators of the group modulo torsion
j	-504871936/394875	j-invariant
L	3.8619574245157	L(r)(E,1)/r!
Ω	0.77610721249322	Real period
R	0.62200772044581	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	15600t1 62400cm1 23400s1 1560f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7800q1

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	-3	-	1	-6	5	-6	2	-7	3	8	2	1	0	-15	-12	5	6	-13	-12	1	-17

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Quadratic twists for elliptic curve 7800q1

-4	8	-3	5	13
15600t1	62400cm1	23400s1	1560f1	101400i1

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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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