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	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	1872 = 24 · 32 · 13	Discriminant
Eigenvalues	2+ 3+ -2  4  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-39,108]	[a1,a2,a3,a4,a6]
j	420616192/117	j-invariant
L	1.1450002182025	L(r)(E,1)/r!
Ω	4.58000087281	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	624f1 2496i1 936i1 7800u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312d1

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 312d1

-4	8	-3	5	-7	-11	13	17	-19
624f1	2496i1	936i1	7800u1	15288j1	37752r1	4056m1	90168o1	112632y1

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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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