Properties

Label 226512.cg
Number of curves $4$
Conductor $226512$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 226512.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
226512.cg1 226512bc4 \([0, 0, 0, -1135618275, 14728264733666]\) \(30618029936661765625/3678951124992\) \(19461109913369327129591808\) \([2]\) \(79626240\) \(3.8772\)  
226512.cg2 226512bc3 \([0, 0, 0, -65087715, 269893096418]\) \(-5764706497797625/2612665516032\) \(-13820615998120689578016768\) \([2]\) \(39813120\) \(3.5307\)  
226512.cg3 226512bc2 \([0, 0, 0, -31372275, -38534337358]\) \(645532578015625/252306960048\) \(1334666679327763261489152\) \([2]\) \(26542080\) \(3.3279\)  
226512.cg4 226512bc1 \([0, 0, 0, 6263565, -4338413134]\) \(5137417856375/4510142208\) \(-23857988392005368020992\) \([2]\) \(13271040\) \(2.9813\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 226512.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 226512.cg do not have complex multiplication.

Modular form 226512.2.a.cg

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - q^{13} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.