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	13650ba	Isogeny class
Conductor	13650	Conductor
∏ cp	126	Product of Tamagawa factors cp
deg	163296	Modular degree for the optimal curve
Δ	-42363211761807300 = -1 · 22 · 39 · 52 · 73 · 137	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -2 13-  7 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,32344,9648938]	[a1,a2,a3,a4,a6]
Generators	[543:-13961:1]	Generators of the group modulo torsion
j	149687036429469215/1694528470472292	j-invariant
L	3.9978077551016	L(r)(E,1)/r!
Ω	0.26643327997787	Real period
R	0.11908659826442	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	109200dy1 40950dx1 13650ce1 95550r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13650ba1

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	-	7	-6	-9	2	-6	2	4	4	3	4	7	2	-9	10	11	8	-12	4	-17

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Quadratic twists for elliptic curve 13650ba1

-4	-3	5	-7
109200dy1	40950dx1	13650ce1	95550r1

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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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