Properties

Label 271440cd
Number of curves $4$
Conductor $271440$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 271440cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.cd3 271440cd1 \([0, 0, 0, -255243, 49632442]\) \(615882348586441/21715200\) \(64841239756800\) \([2]\) \(2359296\) \(1.7400\) \(\Gamma_0(N)\)-optimal
271440.cd2 271440cd2 \([0, 0, 0, -266763, 44906938]\) \(703093388853961/115124490000\) \(343759885148160000\) \([2, 2]\) \(4718592\) \(2.0866\)  
271440.cd4 271440cd3 \([0, 0, 0, 484917, 252220282]\) \(4223169036960119/11647532812500\) \(-34779346617600000000\) \([2]\) \(9437184\) \(2.4332\)  
271440.cd1 271440cd4 \([0, 0, 0, -1202763, -464838662]\) \(64443098670429961/6032611833300\) \(18013282412444467200\) \([2]\) \(9437184\) \(2.4332\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271440cd have rank \(0\).

Complex multiplication

The elliptic curves in class 271440cd do not have complex multiplication.

Modular form 271440.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - 4 q^{11} + q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\)  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.