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

• Label: 137904bu
• Number of curves: $6$
• Conductor: $137904$
• CM: no
• Rank: $1$

Elliptic curves in class 137904bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137904.bh5	137904bu1	$[0, -1, 0, -91992, -9929232]$	$4354703137/352512$	$6969377153875968$	$[2]$	$884736$	$1.7830$	$\Gamma_0(N)$-optimal
137904.bh4	137904bu2	$[0, -1, 0, -308312, 54447600]$	$163936758817/30338064$	$599802021305450496$	$[2, 2]$	$1769472$	$2.1296$
137904.bh2	137904bu3	$[0, -1, 0, -4688792, 3909270000]$	$576615941610337/27060804$	$535008593078009856$	$[2, 2]$	$3538944$	$2.4761$
137904.bh6	137904bu4	$[0, -1, 0, 611048, 316281328]$	$1276229915423/2927177028$	$-57872074438015598592$	$[2]$	$3538944$	$2.4761$
137904.bh1	137904bu5	$[0, -1, 0, -75019832, 250124174832]$	$2361739090258884097/5202$	$102846711472128$	$[2]$	$7077888$	$2.8227$
137904.bh3	137904bu6	$[0, -1, 0, -4445432, 4332911088]$	$-491411892194497/125563633938$	$-2482469594581581176832$	$[2]$	$7077888$	$2.8227$

Rank

The elliptic curves in class 137904bu have rank $1$.

Complex multiplication

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

Modular form 137904.2.a.bu

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.