Properties

Label 115920.h
Number of curves $2$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 115920.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.h1 115920c1 \([0, 0, 0, -783, -2322]\) \(10536048/5635\) \(28393908480\) \([2]\) \(92160\) \(0.69705\) \(\Gamma_0(N)\)-optimal
115920.h2 115920c2 \([0, 0, 0, 2997, -18198]\) \(147704148/92575\) \(-1865885414400\) \([2]\) \(184320\) \(1.0436\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.h have rank \(0\).

Complex multiplication

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

Modular form 115920.2.a.h

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