Cremona's table of elliptic curves

310 = 2 · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	310b	Isogeny class
Conductor	310	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	443751840500 = 22 · 53 · 316	Discriminant
Eigenvalues	2- -2 5+ -4  0 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2046,15376]	[a1,a2,a3,a4,a6]
Generators	[0:124:1]	Generators of the group modulo torsion
j	947226559343329/443751840500	j-invariant
L	1.64151219334	L(r)(E,1)/r!
Ω	0.83954588316873	Real period
R	0.65174607139769	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	2480i4 9920o4 2790m4 1550d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 310b4

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	-4	0	-4	-6	6	-	8	-6	-10	0	0	-12	14	8	0	-4	8	6	-18	-10

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Quadratic twists for elliptic curve 310b4

-4	8	-3	5	-7	-11	13	17	-19	-31
2480i4	9920o4	2790m4	1550d4	15190bd4	37510e4	52390c4	89590m4	111910a4	9610a4

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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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