Cremona's table of elliptic curves

306 = 2 · 3² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17+	Signs for the Atkin-Lehner involutions
Class	306c	Isogeny class
Conductor	306	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	256981248 = 28 · 310 · 17	Discriminant
Eigenvalues	2+ 3-  2  0  4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-306,-1836]	[a1,a2,a3,a4,a6]
j	4354703137/352512	j-invariant
L	1.1471740368869	L(r)(E,1)/r!
Ω	1.1471740368869	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2448n1 9792k1 102b1 7650bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 306c1

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	0	4	-2	+	4	0	10	8	-2	-10	12	0	-6	-12	-10	-12	0	10	-8	-4	6	-14

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Quadratic twists for elliptic curve 306c1

-4	8	-3	5	-7	-11	13	17	-19
2448n1	9792k1	102b1	7650bz1	14994bh1	37026bj1	51714p1	5202b1	110466bj1

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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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