Cremona's table of elliptic curves

13950 = 2 · 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 31+	Signs for the Atkin-Lehner involutions
Class	13950cf	Isogeny class
Conductor	13950	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	-5206809600000000 = -1 · 216 · 38 · 58 · 31	Discriminant
Eigenvalues	2- 3- 5+  0  4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,13495,3415497]	[a1,a2,a3,a4,a6]
Generators	[39:1980:1]	Generators of the group modulo torsion
j	23862997439/457113600	j-invariant
L	7.3654100311956	L(r)(E,1)/r!
Ω	0.32125112206302	Real period
R	0.71647707250563	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	111600ev1 4650a1 2790g1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13950cf1

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	4	-6	2	4	-8	-6	+	2	-10	4	0	-10	12	-2	4	0	-2	0	4	14	-18

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Quadratic twists for elliptic curve 13950cf1

-4	-3	5
111600ev1	4650a1	2790g1

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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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