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Properties

Label 190575.fb
Number of curves $2$
Conductor $190575$
CM no
Rank $1$
Graph

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

Elliptic curves in class 190575.fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.fb1 190575em2 \([0, 0, 1, -1839003375, 12985027823281]\) \(1363413585016606720/644626239703677\) \(325200836153990194149223828125\) \([]\) \(253440000\) \(4.3570\)  
190575.fb2 190575em1 \([0, 0, 1, -947166825, -11219870147819]\) \(116423188793017446400/91315917\) \(73707238665851608125\) \([]\) \(50688000\) \(3.5523\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.fb have rank \(1\).

Complex multiplication

The elliptic curves in class 190575.fb do not have complex multiplication.

Modular form 190575.2.a.fb

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + q^{7} - q^{13} + 2 q^{14} - 4 q^{16} - 3 q^{17} - 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.