Properties

Label 115920.du
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("du1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.du1 115920bl1 \([0, 0, 0, -20658567, 36140450726]\) \(5224645130090610708304/67370009765625\) \(12572860702500000000\) \([2]\) \(6881280\) \(2.8100\) \(\Gamma_0(N)\)-optimal
115920.du2 115920bl2 \([0, 0, 0, -20096067, 38201338226]\) \(-1202345928696155427076/148724718496003125\) \(-111022407458392348800000\) \([2]\) \(13762560\) \(3.1566\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.du have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.du do not have complex multiplication.

Modular form 115920.2.a.du

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 6 q^{11} - 4 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.