Properties

Label 115920.fb
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.fb1 115920ew4 \([0, 0, 0, -727347, 238755634]\) \(14251520160844849/264449745\) \(789642707374080\) \([2]\) \(983040\) \(1.9835\)  
115920.fb2 115920ew2 \([0, 0, 0, -46947, 3473314]\) \(3832302404449/472410225\) \(1410609373286400\) \([2, 2]\) \(491520\) \(1.6369\)  
115920.fb3 115920ew1 \([0, 0, 0, -11667, -428654]\) \(58818484369/7455105\) \(22260824248320\) \([2]\) \(245760\) \(1.2903\) \(\Gamma_0(N)\)-optimal
115920.fb4 115920ew3 \([0, 0, 0, 68973, 17916946]\) \(12152722588271/53476250625\) \(-159679228746240000\) \([2]\) \(983040\) \(1.9835\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.fb

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.