Elliptic curve isogeny class with Cremona label 137904bh (LMFDB label 137904.o)

• Label: 137904bh
• Number of curves: $4$
• Conductor: $137904$
• CM: no
• Rank: $0$

Elliptic curves in class 137904bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137904.o2	137904bh1	\([0, -1, 0, -532913, -149559060]\)	\(216727177216000/2738853\)	\(211518724961232\)	\([2]\)	\(967680\)	\(1.8950\)	\(\Gamma_0(N)\)-optimal
137904.o3	137904bh2	\([0, -1, 0, -518548, -158017172]\)	\(-12479332642000/1526829993\)	\(-1886647488430678272\)	\([2]\)	\(1935360\)	\(2.2416\)
137904.o1	137904bh3	\([0, -1, 0, -837113, 40073136]\)	\(840033089536000/477272151837\)	\(36859224286979170128\)	\([2]\)	\(2903040\)	\(2.4444\)
137904.o4	137904bh4	\([0, -1, 0, 3314372, 315731740]\)	\(3258571509326000/1920843121977\)	\(-2373514974399150436608\)	\([2]\)	\(5806080\)	\(2.7909\)

Rank

The elliptic curves in class 137904bh have rank \(0\).

Complex multiplication

The elliptic curves in class 137904bh do not have complex multiplication.

Modular form 137904.2.a.bh

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.