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	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-73008 = -1 · 24 · 33 · 132	Discriminant
Eigenvalues	2- 3- -4 -4 -2 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5,14]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	702464/4563	j-invariant
L	1.5607603031014	L(r)(E,1)/r!
Ω	2.505687221537	Real period
R	0.20762904080582	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	624b1 2496g1 936c1 7800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312f1

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 312f1

-4	8	-3	5	-7	-11	13	17	-19
624b1	2496g1	936c1	7800b1	15288ba1	37752l1	4056h1	90168r1	112632f1

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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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