Properties

Label 55825l
Number of curves $4$
Conductor $55825$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55825l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55825.t4 55825l1 \([1, -1, 0, 14608, 770891]\) \(22062729659823/29354283343\) \(-458660677234375\) \([2]\) \(172032\) \(1.4991\) \(\Gamma_0(N)\)-optimal
55825.t3 55825l2 \([1, -1, 0, -90517, 7604016]\) \(5249244962308257/1448621666569\) \(22634713540140625\) \([2, 2]\) \(344064\) \(1.8457\)  
55825.t2 55825l3 \([1, -1, 0, -529142, -141967109]\) \(1048626554636928177/48569076788309\) \(758891824817328125\) \([2]\) \(688128\) \(2.1922\)  
55825.t1 55825l4 \([1, -1, 0, -1333892, 593233641]\) \(16798320881842096017/2132227789307\) \(33316059207921875\) \([2]\) \(688128\) \(2.1922\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55825l have rank \(1\).

Complex multiplication

The elliptic curves in class 55825l do not have complex multiplication.

Modular form 55825.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{7} - 3q^{8} - 3q^{9} - q^{11} - 6q^{13} + q^{14} - q^{16} + 2q^{17} - 3q^{18} - 8q^{19} + O(q^{20})\)  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.