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	312f	Isogeny class
Conductor	312	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	2426112 = 28 · 36 · 13	Discriminant
Eigenvalues	2- 3- -4 -4 -2 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-60,144]	[a1,a2,a3,a4,a6]
Generators	[-6:18:1]	Generators of the group modulo torsion
j	94875856/9477	j-invariant
L	1.5607603031014	L(r)(E,1)/r!
Ω	2.505687221537	Real period
R	0.10381452040291	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	624b2 2496g2 936c2 7800b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312f2

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

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Quadratic twists for elliptic curve 312f2

-4	8	-3	5	-7	-11	13	17	-19
624b2	2496g2	936c2	7800b2	15288ba2	37752l2	4056h2	90168r2	112632f2

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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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