Cremona's table of elliptic curves

31312 = 2⁴ · 19 · 103

Field	Data	Notes
Atkin-Lehner	2+ 19+ 103+	Signs for the Atkin-Lehner involutions
Class	31312b	Isogeny class
Conductor	31312	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	17664	Modular degree for the optimal curve
Δ	-13745216512 = -1 · 210 · 194 · 103	Discriminant
Eigenvalues	2+  2  0  0 -2  6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-928,-11952]	[a1,a2,a3,a4,a6]
Generators	[27414:4538898:1]	Generators of the group modulo torsion
j	-86404346500/13423063	j-invariant
L	8.1695441564611	L(r)(E,1)/r!
Ω	0.42878873868507	Real period
R	9.5263044704884	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15656h1 125248bl1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 31312b1

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

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Quadratic twists for elliptic curve 31312b1

-4	8
15656h1	125248bl1

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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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