Properties

Label 127296j
Number of curves $4$
Conductor $127296$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 127296j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127296.l4 127296j1 \([0, 0, 0, -1416, -54200]\) \(-420616192/1456611\) \(-1087354285056\) \([2]\) \(196608\) \(0.99561\) \(\Gamma_0(N)\)-optimal
127296.l3 127296j2 \([0, 0, 0, -31836, -2183600]\) \(298766385232/439569\) \(5250184003584\) \([2, 2]\) \(393216\) \(1.3422\)  
127296.l2 127296j3 \([0, 0, 0, -41196, -794576]\) \(161838334948/87947613\) \(4201762644099072\) \([2]\) \(786432\) \(1.6888\)  
127296.l1 127296j4 \([0, 0, 0, -509196, -139854224]\) \(305612563186948/663\) \(31675318272\) \([2]\) \(786432\) \(1.6888\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127296j have rank \(0\).

Complex multiplication

The elliptic curves in class 127296j do not have complex multiplication.

Modular form 127296.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{7} - 4 q^{11} - q^{13} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.