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	312d	Isogeny class
Conductor	312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3504384 = 28 · 34 · 132	Discriminant
Eigenvalues	2+ 3+ -2  4  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-44,84]	[a1,a2,a3,a4,a6]
j	37642192/13689	j-invariant
L	1.1450002182025	L(r)(E,1)/r!
Ω	2.290000436405	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	624f2 2496i2 936i2 7800u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312d2

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

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Quadratic twists for elliptic curve 312d2

-4	8	-3	5	-7	-11	13	17	-19
624f2	2496i2	936i2	7800u2	15288j2	37752r2	4056m2	90168o2	112632y2

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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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