Cremona's table of elliptic curves

1023 = 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	3+ 11- 31+	Signs for the Atkin-Lehner involutions
Class	1023a	Isogeny class
Conductor	1023	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	6840	Modular degree for the optimal curve
Δ	3859200593875737 = 33 · 115 · 316	Discriminant
Eigenvalues	1 3+ -2 -2 11-  4 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-100521,11855376]	[a1,a2,a3,a4,a6]
j	112331320422638310937/3859200593875737	j-invariant
L	1.0960861662256	L(r)(E,1)/r!
Ω	0.43843446649024	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	16368w1 65472p1 3069a1 25575m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1023a1

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
1	+	-2	-2	-	4	-2	6	-4	6	+	6	10	12	2	0	2	-12	8	-6	16	-16	-12	-12	14

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Quadratic twists for elliptic curve 1023a1

-4	8	-3	5	-7	-11	-31
16368w1	65472p1	3069a1	25575m1	50127r1	11253a1	31713d1

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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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