Elliptic curve isogeny class with LMFDB label 338.f (Cremona label 338c)

• Label: 338.f
• Number of curves: $3$
• Conductor: $338$
• CM: no
• Rank: $0$

Elliptic curves in class 338.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338.f1	338c3	$[1, 0, 0, -77659, -8336303]$	$-10730978619193/6656$	$-32127240704$	$[]$	$1008$	$1.3369$
338.f2	338c2	$[1, 0, 0, -764, -16264]$	$-10218313/17576$	$-84835994984$	$[]$	$336$	$0.78755$
338.f3	338c1	$[1, 0, 0, 81, 467]$	$12167/26$	$-125497034$	$[]$	$112$	$0.23825$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 338.f have rank $0$.

Complex multiplication

The elliptic curves in class 338.f do not have complex multiplication.

Modular form 338.2.a.f

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.