Cremona's table of elliptic curves

33 = 3 · 11

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Conductor	33	Conductor
Count	4	Number of curves in isogeny class
Curves	33a1 33a2 33a3 33a4	Curves in isogeny class
deg	3	Modular degree for the optimal curve
Eigenvalues	1 3+ -2  4 11- -2 -2  0	Hecke eigenvalues for primes less than 20
L	0.74733914774274	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	528h 2112l 99b 825b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 33a

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	+	-2	4	-	-2	-2	0	8	-6	-8	6	-2	0	8	6	-4	6	-4	0	-14	-4	12	-6	2

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Quadratic twists for isogeny class 33a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
528h	2112l	99b	825b	1617j	363a	5577d	9537j	11913i	17457a	27753d	31713e	45177a	55473l	61017a	72897a	92697e	114873c	122793a

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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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