Elliptic curve isogeny class with Cremona label 16905c (LMFDB label 16905.e)

• Label: 16905c
• Number of curves: $4$
• Conductor: $16905$
• CM: no
• Rank: $0$

Elliptic curves in class 16905c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16905.e3	16905c1	\([1, 1, 1, -13721, -622546]\)	\(2428257525121/8150625\)	\(958912880625\)	\([2]\)	\(24576\)	\(1.1634\)	\(\Gamma_0(N)\)-optimal
16905.e2	16905c2	\([1, 1, 1, -19846, -19846]\)	\(7347774183121/4251692025\)	\(500207315049225\)	\([2, 2]\)	\(49152\)	\(1.5100\)
16905.e1	16905c3	\([1, 1, 1, -217071, 38715144]\)	\(9614816895690721/34652610405\)	\(4076844961537845\)	\([2]\)	\(98304\)	\(1.8565\)
16905.e4	16905c4	\([1, 1, 1, 79379, -59536]\)	\(470166844956479/272118787605\)	\(-32014503242940645\)	\([2]\)	\(98304\)	\(1.8565\)

Rank

The elliptic curves in class 16905c have rank \(0\).

Complex multiplication

The elliptic curves in class 16905c do not have complex multiplication.

Modular form 16905.2.a.c

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.