Cremona's table of elliptic curves

1204 = 2² · 7 · 43

Field	Data	Notes
Atkin-Lehner	2- 7+ 43-	Signs for the Atkin-Lehner involutions
Class	1204a	Isogeny class
Conductor	1204	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2208	Modular degree for the optimal curve
Δ	-63458929408 = -1 · 28 · 78 · 43	Discriminant
Eigenvalues	2-  2 -4 7+  5 -1 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4445,-113239]	[a1,a2,a3,a4,a6]
Generators	[595:14406:1]	Generators of the group modulo torsion
j	-37948686032896/247886443	j-invariant
L	2.8663638151071	L(r)(E,1)/r!
Ω	0.29222943802649	Real period
R	1.6347678924617	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	4816f1 19264h1 10836f1 30100g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1204a1

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	+	5	-1	-3	-6	-3	-6	-3	0	-3	-	-12	-1	-4	2	3	6	2	-16	-7	12	-1

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Quadratic twists for elliptic curve 1204a1

-4	8	-3	5	-7	-43
4816f1	19264h1	10836f1	30100g1	8428c1	51772c1

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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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