Cremona's table of elliptic curves

312 = 2³ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	312c	Isogeny class
Conductor	312	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	39936 = 210 · 3 · 13	Discriminant
Eigenvalues	2- 3-  2  0  0 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-832,-9520]	[a1,a2,a3,a4,a6]
j	62275269892/39	j-invariant
L	1.7776867882324	L(r)(E,1)/r!
Ω	0.88884339411621	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	624c3 2496c3 936e3 7800a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312c3

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

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Quadratic twists for elliptic curve 312c3

-4	8	-3	5	-7	-11	13	17	-19
624c3	2496c3	936e3	7800a3	15288v3	37752i4	4056f3	90168v4	112632b4

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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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