Elliptic curve isogeny class with LMFDB label 164331.a (Cremona label 164331a)

• Label: 164331.a
• Number of curves: $4$
• Conductor: $164331$
• CM: no
• Rank: $1$

Elliptic curves in class 164331.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164331.a1	164331a3	$[1, -1, 1, -878054, 316902498]$	$115714886617/1539$	$995717892328011$	$[2]$	$1382400$	$2.0213$
164331.a2	164331a2	$[1, -1, 1, -56399, 4673598]$	$30664297/3249$	$2102071106025801$	$[2, 2]$	$691200$	$1.6747$
164331.a3	164331a1	$[1, -1, 1, -13154, -498504]$	$389017/57$	$36878440456593$	$[2]$	$345600$	$1.3281$	$\Gamma_0(N)$-optimal
164331.a4	164331a4	$[1, -1, 1, 73336, 22940286]$	$67419143/390963$	$-252949223091771387$	$[2]$	$1382400$	$2.0213$

Rank

The elliptic curves in class 164331.a have rank $1$.

Complex multiplication

The elliptic curves in class 164331.a do not have complex multiplication.

Modular form 164331.2.a.a

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.