Cremona's table of elliptic curves

69312 = 2⁶ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19+	Signs for the Atkin-Lehner involutions
Class	69312bz	Isogeny class
Conductor	69312	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	758550528 = 212 · 33 · 193	Discriminant
Eigenvalues	2- 3+  0  0  2 -6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-633,6201]	[a1,a2,a3,a4,a6]
Generators	[-25:76:1] [-5:96:1]	Generators of the group modulo torsion
j	1000000/27	j-invariant
L	9.0740738921406	L(r)(E,1)/r!
Ω	1.5928871192567	Real period
R	2.8483103989072	Regulator
r	2	Rank of the group of rational points
S	1.0000000000013	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69312cx1 34656y1 69312cw1	Quadratic twists by: -4 8 -19

Hecke Eigenvalues for elliptic curve 69312bz1

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

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Quadratic twists for elliptic curve 69312bz1

-4	8	-19
69312cx1	34656y1	69312cw1

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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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