Cremona's table of elliptic curves

318 = 2 · 3 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3+ 53+	Signs for the Atkin-Lehner involutions
Class	318c	Isogeny class
Conductor	318	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-77274 = -1 · 2 · 36 · 53	Discriminant
Eigenvalues	2+ 3+ -1  0 -1 -2 -7  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,7,-9]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	30080231/77274	j-invariant
L	1.1170141948269	L(r)(E,1)/r!
Ω	1.7722504260997	Real period
R	0.31514005537162	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	2544e1 10176j1 954l1 7950bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 318c1

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	-1	-2	-7	2	-5	-4	-1	-2	-4	-1	6	+	9	10	-2	0	10	1	6	-1	-13

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Quadratic twists for elliptic curve 318c1

-4	8	-3	5	-7	-11	13	17	-19	53
2544e1	10176j1	954l1	7950bs1	15582i1	38478g1	53742m1	91902h1	114798z1	16854q1

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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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