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	26400a	Isogeny class
Conductor	26400	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	2205225000000 = 26 · 36 · 58 · 112	Discriminant
Eigenvalues	2+ 3+ 5+  0 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24758,-1489488]	[a1,a2,a3,a4,a6]
Generators	[7706:235625:8]	Generators of the group modulo torsion
j	1678370855104/2205225	j-invariant
L	4.5159826228337	L(r)(E,1)/r!
Ω	0.38063039805345	Real period
R	5.9322411530037	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	26400t1 52800gs2 79200dt1 5280p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 26400a1

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	+	2	-2	-4	8	6	8	-2	-2	-8	-8	-14	4	10	4	4	-10	8	-4	2	-18

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Quadratic twists for elliptic curve 26400a1

-4	8	-3	5
26400t1	52800gs2	79200dt1	5280p1

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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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