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	312b	Isogeny class
Conductor	312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-129792 = -1 · 28 · 3 · 132	Discriminant
Eigenvalues	2+ 3+  0 -4 -2 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,-12]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	686000/507	j-invariant
L	1.4061524822049	L(r)(E,1)/r!
Ω	1.8449376483454	Real period
R	0.76216802419637	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	624d2 2496m2 936h2 7800w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 312b2

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

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Quadratic twists for elliptic curve 312b2

-4	8	-3	5	-7	-11	13	17	-19
624d2	2496m2	936h2	7800w2	15288l2	37752s2	4056k2	90168k2	112632ba2

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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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