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Properties

Label 56550.l
Number of curves $2$
Conductor $56550$
CM no
Rank $0$
Graph

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

Elliptic curves in class 56550.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.l1 56550n1 \([1, 1, 0, -4500, -127650]\) \(-16129912968025/1599869622\) \(-999918513750\) \([]\) \(114000\) \(1.0431\) \(\Gamma_0(N)\)-optimal
56550.l2 56550n2 \([1, 1, 0, 4925, 8702125]\) \(33809954855/83728056672\) \(-32706272137500000\) \([]\) \(570000\) \(1.8478\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56550.l have rank \(0\).

Complex multiplication

The elliptic curves in class 56550.l do not have complex multiplication.

Modular form 56550.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} - 3 q^{11} - q^{12} - q^{13} - 2 q^{14} + q^{16} + 7 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.