Cremona's table of elliptic curves

1035 = 3² · 5 · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	1035a	Isogeny class
Conductor	1035	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-13751035875 = -1 · 314 · 53 · 23	Discriminant
Eigenvalues	2 3- 5+ -5  2 -6 -1  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-903,-11871]	[a1,a2,a3,a4,a6]
Generators	[418:2309:8]	Generators of the group modulo torsion
j	-111701610496/18862875	j-invariant
L	3.9154903036292	L(r)(E,1)/r!
Ω	0.43147339703196	Real period
R	4.5373484559689	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16560bo1 66240dh1 345f1 5175h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1035a1

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	-	+	-5	2	-6	-1	2	-	1	-5	-7	7	-8	12	-9	-3	12	-1	-5	-2	-8	-3	-8	14

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Quadratic twists for elliptic curve 1035a1

-4	8	-3	5	-7	-11	-23
16560bo1	66240dh1	345f1	5175h1	50715bt1	125235bd1	23805v1

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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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