Cremona's table of elliptic curves

31200 = 2⁵ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	31200bq	Isogeny class
Conductor	31200	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	10281960000000 = 29 · 32 · 57 · 134	Discriminant
Eigenvalues	2- 3+ 5+ -4  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13408,581812]	[a1,a2,a3,a4,a6]
Generators	[-92:1014:1]	Generators of the group modulo torsion
j	33324076232/1285245	j-invariant
L	3.8826414634115	L(r)(E,1)/r!
Ω	0.71725366599731	Real period
R	1.3533013658469	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31200cg3 62400gu3 93600bx3 6240k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 31200bq3

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
-	+	+	-4	4	-	-2	-4	0	6	0	-10	2	4	-4	6	-4	-2	4	-8	2	16	-4	10	2

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Quadratic twists for elliptic curve 31200bq3

-4	8	-3	5
31200cg3	62400gu3	93600bx3	6240k3

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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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