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	312a	Isogeny class
Conductor	312	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-8112 = -1 · 24 · 3 · 132	Discriminant
Eigenvalues	2+ 3-  0  0  6 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3,-6]	[a1,a2,a3,a4,a6]
j	-256000/507	j-invariant
L	1.6605942610394	L(r)(E,1)/r!
Ω	1.6605942610394	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	624a1 2496d1 936g1 7800p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312a1

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
+	-	0	0	6	+	2	0	4	-6	-4	-2	0	4	10	-10	-6	-6	-12	2	6	-16	6	4	14

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Quadratic twists for elliptic curve 312a1

-4	8	-3	5	-7	-11	13	17	-19
624a1	2496d1	936g1	7800p1	15288f1	37752v1	4056p1	90168a1	112632r1

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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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