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	16	Product of Tamagawa factors cp
Δ	389376 = 28 · 32 · 132	Discriminant
Eigenvalues	2- 3-  2  0  0 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-52,-160]	[a1,a2,a3,a4,a6]
j	61918288/1521	j-invariant
L	1.7776867882324	L(r)(E,1)/r!
Ω	1.7776867882324	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	624c2 2496c2 936e2 7800a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312c2

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 312c2

-4	8	-3	5	-7	-11	13	17	-19
624c2	2496c2	936e2	7800a2	15288v2	37752i2	4056f2	90168v2	112632b2

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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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