Properties

Label 55825.l
Number of curves $2$
Conductor $55825$
CM no
Rank $2$
Graph

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

Elliptic curves in class 55825.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55825.l1 55825d1 \([0, -1, 1, -1583, 37068]\) \(-28094464000/20657483\) \(-322773171875\) \([]\) \(48384\) \(0.90779\) \(\Gamma_0(N)\)-optimal
55825.l2 55825d2 \([0, -1, 1, 12917, -568307]\) \(15252992000000/17621717267\) \(-275339332296875\) \([]\) \(145152\) \(1.4571\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55825.l have rank \(2\).

Complex multiplication

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

Modular form 55825.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{7} - 2 q^{9} - q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{16} - 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.