Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.fh1 115920ey2 \([0, 0, 0, -141627, -20514454]\) \(105214211150329/2028600\) \(6057367142400\) \([2]\) \(442368\) \(1.5755\)  
115920.fh2 115920ey1 \([0, 0, 0, -9147, -298006]\) \(28344726649/3554880\) \(10614814801920\) \([2]\) \(221184\) \(1.2289\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.fh

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