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	26400bn	Isogeny class
Conductor	26400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	38400	Modular degree for the optimal curve
Δ	-9107873280000 = -1 · 212 · 35 · 54 · 114	Discriminant
Eigenvalues	2- 3+ 5- -1 11+ -3  0 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1133,-145563]	[a1,a2,a3,a4,a6]
Generators	[583:14036:1]	Generators of the group modulo torsion
j	-62886400/3557763	j-invariant
L	3.8349365376281	L(r)(E,1)/r!
Ω	0.32089020141374	Real period
R	2.9877326580342	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	26400cf1 52800hr1 79200cf1 26400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 26400bn1

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	0	-3	4	4	-5	-6	2	-1	6	6	10	-5	7	6	-14	0	14	12	-11

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Quadratic twists for elliptic curve 26400bn1

-4	8	-3	5
26400cf1	52800hr1	79200cf1	26400o1

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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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