Properties

Label 55440dc
Number of curves $4$
Conductor $55440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 55440dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.b4 55440dc1 \([0, 0, 0, -4203, -1109862]\) \(-2749884201/176619520\) \(-527383060807680\) \([2]\) \(196608\) \(1.5047\) \(\Gamma_0(N)\)-optimal
55440.b3 55440dc2 \([0, 0, 0, -188523, -31301478]\) \(248158561089321/1859334400\) \(5551942769049600\) \([2, 2]\) \(393216\) \(1.8513\)  
55440.b2 55440dc3 \([0, 0, 0, -315243, 16066458]\) \(1160306142246441/634128110000\) \(1893496390410240000\) \([2]\) \(786432\) \(2.1978\)  
55440.b1 55440dc4 \([0, 0, 0, -3010923, -2010932838]\) \(1010962818911303721/57392720\) \(171373743636480\) \([2]\) \(786432\) \(2.1978\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55440dc have rank \(1\).

Complex multiplication

The elliptic curves in class 55440dc do not have complex multiplication.

Modular form 55440.2.a.dc

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.