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	7800t	Isogeny class
Conductor	7800	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	123383520000000 = 211 · 33 · 57 · 134	Discriminant
Eigenvalues	2- 3- 5+  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-145408,21286688]	[a1,a2,a3,a4,a6]
Generators	[323:2850:1]	Generators of the group modulo torsion
j	10625310339698/3855735	j-invariant
L	5.2560816453418	L(r)(E,1)/r!
Ω	0.57702054619846	Real period
R	3.0363341940884	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	15600d3 62400y4 23400g4 1560a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7800t4

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	+	2	-4	-4	-6	-4	-6	-2	-12	-8	-14	12	-2	0	8	2	8	-12	6	10

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Quadratic twists for elliptic curve 7800t4

-4	8	-3	5	13
15600d3	62400y4	23400g4	1560a4	101400bb4

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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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