Elliptic curve isogeny class with LMFDB label 1638.l (Cremona label 1638t)

• Label: 1638.l
• Number of curves: $3$
• Conductor: $1638$
• CM: no
• Rank: $1$

Elliptic curves in class 1638.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1638.l1	1638t3	$[1, -1, 1, -234509, 43769909]$	$-1956469094246217097/36641439744$	$-26711609573376$	$[3]$	$15552$	$1.7008$
1638.l2	1638t2	$[1, -1, 1, -1094, 133589]$	$-198461344537/10417365504$	$-7594259452416$	$[3]$	$5184$	$1.1515$
1638.l3	1638t1	$[1, -1, 1, 121, -4921]$	$270840023/14329224$	$-10446004296$	$[]$	$1728$	$0.60215$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1638.l have rank $1$.

Complex multiplication

The elliptic curves in class 1638.l do not have complex multiplication.

Modular form 1638.2.a.l

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.