Elliptic curve isogeny class with Cremona label 1760f (LMFDB label 1760.h)

• Label: 1760f
• Number of curves: $4$
• Conductor: $1760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1760f have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1760f do not have complex multiplication.

Modular form 1760.2.a.f

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 1760f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1760.h3	1760f1	\([0, 0, 0, -37, 84]\)	\(87528384/3025\)	\(193600\)	\([2, 2]\)	\(128\)	\(-0.21400\)	\(\Gamma_0(N)\)-optimal
1760.h2	1760f2	\([0, 0, 0, -92, -224]\)	\(21024576/6875\)	\(28160000\)	\([2]\)	\(256\)	\(0.13258\)
1760.h1	1760f3	\([0, 0, 0, -587, 5474]\)	\(43688592648/55\)	\(28160\)	\([2]\)	\(256\)	\(0.13258\)
1760.h4	1760f4	\([0, 0, 0, 13, 294]\)	\(474552/73205\)	\(-37480960\)	\([4]\)	\(256\)	\(0.13258\)