Cremona's table of elliptic curves

2405 = 5 · 13 · 37

Field	Data	Notes
Atkin-Lehner	5+ 13+ 37+	Signs for the Atkin-Lehner involutions
Class	2405a	Isogeny class
Conductor	2405	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	904187708125 = 54 · 134 · 373	Discriminant
Eigenvalues	2  1 5+ -1 -1 13+ -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-5526,149521]	[a1,a2,a3,a4,a6]
Generators	[-214:4221:8]	Generators of the group modulo torsion
j	18665298626719744/904187708125	j-invariant
L	6.022360323338	L(r)(E,1)/r!
Ω	0.87489877039636	Real period
R	1.7208734676269	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	38480k1 21645o1 12025f1 117845o1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2405a1

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	1	+	-1	-1	+	-4	0	-6	2	-4	+	3	10	7	5	0	8	8	-3	-9	-12	-7	-4	-8

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Quadratic twists for elliptic curve 2405a1

-4	-3	5	-7	13	37
38480k1	21645o1	12025f1	117845o1	31265g1	88985j1

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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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