Cremona's table of elliptic curves

780 = 2² · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13+	Signs for the Atkin-Lehner involutions
Class	780a	Isogeny class
Conductor	780	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	421200 = 24 · 34 · 52 · 13	Discriminant
Eigenvalues	2- 3+ 5- -2 -2 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-105,450]	[a1,a2,a3,a4,a6]
Generators	[15:-45:1]	Generators of the group modulo torsion
j	8077950976/26325	j-invariant
L	2.0100038392987	L(r)(E,1)/r!
Ω	2.996574847856	Real period
R	0.22358903541008	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	3120w1 12480bc1 2340e1 3900k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 780a1

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	-2	+	-2	-2	-4	2	-2	-6	-2	-8	-6	6	6	-2	-14	-6	-6	4	6	14	-14

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Quadratic twists for elliptic curve 780a1

-4	8	-3	5	-7	-11	13
3120w1	12480bc1	2340e1	3900k1	38220w1	94380j1	10140b1

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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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