Cremona's table of elliptic curves

102 = 2 · 3 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	102a	Isogeny class
Conductor	102	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	612 = 22 · 32 · 17	Discriminant
Eigenvalues	2+ 3+ -4 -2  0 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,0]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	1771561/612	j-invariant
L	0.67728489801667	L(r)(E,1)/r!
Ω	4.7278638235415	Real period
R	0.14325389294088	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	816j1 3264o1 306d1 2550bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 102a1

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
+	+	-4	-2	0	-6	+	4	6	-4	-6	-4	-10	-4	4	-2	12	-4	-12	-6	2	10	-12	-2	6

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Quadratic twists for elliptic curve 102a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
816j1	3264o1	306d1	2550bd1	4998x1	12342y1	17238j1	1734g1	36822bc1	53958m1	85782q1	98022l1

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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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