Elliptic curve isogeny class with LMFDB label 17160.i (Cremona label 17160a)

• Label: 17160.i
• Number of curves: $4$
• Conductor: $17160$
• CM: no
• Rank: $0$

Elliptic curves in class 17160.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17160.i1	17160a4	\([0, -1, 0, -35256, 2559756]\)	\(2366492816943218/23562825\)	\(48256665600\)	\([2]\)	\(40960\)	\(1.2096\)
17160.i2	17160a3	\([0, -1, 0, -7976, -229140]\)	\(27403349188178/4524609375\)	\(9266400000000\)	\([2]\)	\(40960\)	\(1.2096\)
17160.i3	17160a2	\([0, -1, 0, -2256, 38556]\)	\(1240605018436/115025625\)	\(117786240000\)	\([2, 2]\)	\(20480\)	\(0.86303\)
17160.i4	17160a1	\([0, -1, 0, 164, 2740]\)	\(1893932336/14274975\)	\(-3654393600\)	\([2]\)	\(10240\)	\(0.51646\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 17160.i have rank \(0\).

Complex multiplication

The elliptic curves in class 17160.i do not have complex multiplication.

Modular form 17160.2.a.i

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.