Elliptic curve isogeny class with Cremona label 485184q (LMFDB label 485184.q)

• Label: 485184q
• Number of curves: $4$
• Conductor: $485184$
• CM: no
• Rank: $0$

Elliptic curves in class 485184q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485184.q3	485184q1	$[0, -1, 0, -1346289, -600797967]$	$350104249168/2793$	$2152843602051072$	$[2]$	$7372800$	$2.1142$	$\Gamma_0(N)$-optimal^*
485184.q2	485184q2	$[0, -1, 0, -1375169, -573644991]$	$93280467172/7800849$	$24051568722114576384$	$[2, 2]$	$14745600$	$2.4608$	$\Gamma_0(N)$-optimal^*
485184.q1	485184q3	$[0, -1, 0, -4667489, 3222399969]$	$1823652903746/328593657$	$2026239175501652557824$	$[2]$	$29491200$	$2.8074$	$\Gamma_0(N)$-optimal^*
485184.q4	485184q4	$[0, -1, 0, 1455071, -2632361567]$	$55251546334/517244049$	$-3189532521557153415168$	$[2]$	$29491200$	$2.8074$

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 485184q1.

Rank

The elliptic curves in class 485184q have rank $0$.

Complex multiplication

The elliptic curves in class 485184q do not have complex multiplication.

Modular form 485184.2.a.q

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.