Elliptic curve isogeny class with Cremona label 116688g (LMFDB label 116688.t)

• Label: 116688g
• Number of curves: $4$
• Conductor: $116688$
• CM: no
• Rank: $0$

Elliptic curves in class 116688g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
116688.t3	116688g1	\([0, 1, 0, -2244, -38148]\)	\(4883664557392/465796617\)	\(119243933952\)	\([2]\)	\(155648\)	\(0.86318\)	\(\Gamma_0(N)\)-optimal
116688.t2	116688g2	\([0, 1, 0, -8024, 232356]\)	\(55802112308068/8988746481\)	\(9204476396544\)	\([2, 2]\)	\(311296\)	\(1.2098\)
116688.t4	116688g3	\([0, 1, 0, 14416, 1318452]\)	\(161769988460446/457624934481\)	\(-937215865817088\)	\([2]\)	\(622592\)	\(1.5563\)
116688.t1	116688g4	\([0, 1, 0, -122944, 16550996]\)	\(100350446414931074/3407151033\)	\(6977845315584\)	\([4]\)	\(622592\)	\(1.5563\)

Rank

The elliptic curves in class 116688g have rank \(0\).

Complex multiplication

The elliptic curves in class 116688g do not have complex multiplication.

Modular form 116688.2.a.g

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.