Elliptic curve isogeny class with Cremona label 43350dd (LMFDB label 43350.cv)

• Label: 43350dd
• Number of curves: $8$
• Conductor: $43350$
• CM: no
• Rank: $1$

Elliptic curves in class 43350dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43350.cv8	43350dd1	$[1, 0, 0, 10687, 1306617]$	$357911/2160$	$-814642953750000$	$[2]$	$221184$	$1.5430$	$\Gamma_0(N)$-optimal
43350.cv6	43350dd2	$[1, 0, 0, -133813, 17057117]$	$702595369/72900$	$27494199689062500$	$[2, 2]$	$442368$	$1.8896$
43350.cv7	43350dd3	$[1, 0, 0, -97688, -38467008]$	$-273359449/1536000$	$-579301656000000000$	$[2]$	$663552$	$2.0923$
43350.cv5	43350dd4	$[1, 0, 0, -495063, -115521633]$	$35578826569/5314410$	$2004327157332656250$	$[2]$	$884736$	$2.2362$
43350.cv4	43350dd5	$[1, 0, 0, -2084563, 1158245867]$	$2656166199049/33750$	$12728796152343750$	$[2]$	$884736$	$2.2362$
43350.cv3	43350dd6	$[1, 0, 0, -2409688, -1437227008]$	$4102915888729/9000000$	$3394345640625000000$	$[2, 2]$	$1327104$	$2.4389$
43350.cv1	43350dd7	$[1, 0, 0, -38534688, -92074852008]$	$16778985534208729/81000$	$30549110765625000$	$[2]$	$2654208$	$2.7855$
43350.cv2	43350dd8	$[1, 0, 0, -3276688, -310994008]$	$10316097499609/5859375000$	$2209860443115234375000$	$[2]$	$2654208$	$2.7855$

Rank

The elliptic curves in class 43350dd have rank $1$.

Complex multiplication

The elliptic curves in class 43350dd do not have complex multiplication.

Modular form 43350.2.a.dd

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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.