Cremona's table of elliptic curves

61600 = 2⁵ · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	61600bm	Isogeny class
Conductor	61600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-102487000000 = -1 · 26 · 56 · 7 · 114	Discriminant
Eigenvalues	2- -2 5+ 7- 11+  0  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1958,36088]	[a1,a2,a3,a4,a6]
Generators	[-2:200:1]	Generators of the group modulo torsion
j	-830584000/102487	j-invariant
L	3.9350591105412	L(r)(E,1)/r!
Ω	1.0306379208443	Real period
R	1.9090405229041	Regulator
r	1	Rank of the group of rational points
S	0.99999999996806	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	61600bi1 123200gg1 2464b1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 61600bm1

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
-	-2	+	-	+	0	6	-6	0	-6	0	-2	2	4	0	-6	-2	4	-8	16	2	8	-2	-14	-6

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Quadratic twists for elliptic curve 61600bm1

-4	8	5
61600bi1	123200gg1	2464b1

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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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