Elliptic curve isogeny class with Cremona label 350d (LMFDB label 350.f)

• Label: 350d
• Number of curves: $6$
• Conductor: $350$
• CM: no
• Rank: $0$

Elliptic curves in class 350d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
350.f5	350d1	$[1, 1, 1, -13, 31]$	$-15625/28$	$-437500$	$[2]$	$48$	$-0.22737$	$\Gamma_0(N)$-optimal
350.f4	350d2	$[1, 1, 1, -263, 1531]$	$128787625/98$	$1531250$	$[2]$	$96$	$0.11921$
350.f6	350d3	$[1, 1, 1, 112, -719]$	$9938375/21952$	$-343000000$	$[2]$	$144$	$0.32194$
350.f3	350d4	$[1, 1, 1, -888, -8719]$	$4956477625/941192$	$14706125000$	$[2]$	$288$	$0.66851$
350.f2	350d5	$[1, 1, 1, -4263, -109219]$	$-548347731625/1835008$	$-28672000000$	$[2]$	$432$	$0.87125$
350.f1	350d6	$[1, 1, 1, -68263, -6893219]$	$2251439055699625/25088$	$392000000$	$[2]$	$864$	$1.2178$

Rank

The elliptic curves in class 350d have rank $0$.

Complex multiplication

The elliptic curves in class 350d do not have complex multiplication.

Modular form 350.2.a.d

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.