Cremona's table of elliptic curves

26400 = 2⁵ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	26400by	Isogeny class
Conductor	26400	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	27225000000 = 26 · 32 · 58 · 112	Discriminant
Eigenvalues	2- 3- 5+ -4 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-758,-1512]	[a1,a2,a3,a4,a6]
Generators	[-26:36:1]	Generators of the group modulo torsion
j	48228544/27225	j-invariant
L	5.307631697646	L(r)(E,1)/r!
Ω	0.98021577822365	Real period
R	2.7073792401426	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	26400bl1 52800fe2 79200bx1 5280c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 26400by1

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

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Quadratic twists for elliptic curve 26400by1

-4	8	-3	5
26400bl1	52800fe2	79200bx1	5280c1

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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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