Cremona's table of elliptic curves

1236 = 2² · 3 · 103

Field	Data	Notes
Atkin-Lehner	2- 3+ 103-	Signs for the Atkin-Lehner involutions
Class	1236a	Isogeny class
Conductor	1236	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-711936 = -1 · 28 · 33 · 103	Discriminant
Eigenvalues	2- 3+  1  0  0 -5 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-260,1704]	[a1,a2,a3,a4,a6]
Generators	[10:-2:1]	Generators of the group modulo torsion
j	-7622072656/2781	j-invariant
L	2.3745565881218	L(r)(E,1)/r!
Ω	2.8041014376947	Real period
R	0.28227183655595	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	4944i1 19776s1 3708c1 30900f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1236a1

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	0	0	-5	-4	-4	3	0	5	8	-10	5	-8	-6	-9	-5	7	0	-14	-12	11	-10	5

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Quadratic twists for elliptic curve 1236a1

-4	8	-3	5	-7	-103
4944i1	19776s1	3708c1	30900f1	60564g1	127308h1

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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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