Elliptic curve isogeny class with Cremona label 17424t (LMFDB label 17424.bu)

• Label: 17424t
• Number of curves: $6$
• Conductor: $17424$
• CM: no
• Rank: $1$

Elliptic curves in class 17424t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17424.bu5	17424t1	$[0, 0, 0, 726, -9317]$	$2048/3$	$-61990462512$	$[2]$	$10240$	$0.75633$	$\Gamma_0(N)$-optimal
17424.bu4	17424t2	$[0, 0, 0, -4719, -93170]$	$35152/9$	$2975542200576$	$[2, 2]$	$20480$	$1.1029$
17424.bu2	17424t3	$[0, 0, 0, -70059, -7136822]$	$28756228/3$	$3967389600768$	$[2]$	$40960$	$1.4495$
17424.bu3	17424t4	$[0, 0, 0, -26499, 1583890]$	$1556068/81$	$107119519220736$	$[2, 2]$	$40960$	$1.4495$
17424.bu1	17424t5	$[0, 0, 0, -418539, 104219962]$	$3065617154/9$	$23804337604608$	$[2]$	$81920$	$1.7960$
17424.bu6	17424t6	$[0, 0, 0, 17061, 6279658]$	$207646/6561$	$-17353362113759232$	$[2]$	$81920$	$1.7960$

Rank

The elliptic curves in class 17424t have rank $1$.

Complex multiplication

The elliptic curves in class 17424t do not have complex multiplication.

Modular form 17424.2.a.t

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.