Cremona's table of elliptic curves

13650 = 2 · 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	13650a	Isogeny class
Conductor	13650	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	182034216000000000 = 212 · 36 · 59 · 74 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-643125,197182125]	[a1,a2,a3,a4,a6]
Generators	[-735:16905:1]	Generators of the group modulo torsion
j	1882742462388824401/11650189824000	j-invariant
L	2.4905078045159	L(r)(E,1)/r!
Ω	0.32178446072115	Real period
R	1.9349192615877	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	109200fz1 40950dm1 2730bd1 95550ej1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650a1

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

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Quadratic twists for elliptic curve 13650a1

-4	-3	5	-7
109200fz1	40950dm1	2730bd1	95550ej1

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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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