Properties

Label 187425bi
Number of curves $4$
Conductor $187425$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 187425bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187425.bn4 187425bi1 \([1, -1, 1, -1995755, -2465701878]\) \(-656008386769/1581036975\) \(-2118740757864437109375\) \([2]\) \(7077888\) \(2.7802\) \(\Gamma_0(N)\)-optimal
187425.bn3 187425bi2 \([1, -1, 1, -42181880, -105342181878]\) \(6193921595708449/6452105625\) \(8646438620914541015625\) \([2, 2]\) \(14155776\) \(3.1268\)  
187425.bn2 187425bi3 \([1, -1, 1, -52600505, -49310816628]\) \(12010404962647729/6166198828125\) \(8263296168797296142578125\) \([2]\) \(28311552\) \(3.4734\)  
187425.bn1 187425bi4 \([1, -1, 1, -674741255, -6745950500628]\) \(25351269426118370449/27551475\) \(36921611540288671875\) \([2]\) \(28311552\) \(3.4734\)  

Rank

sage: E.rank()
 

The elliptic curves in class 187425bi have rank \(0\).

Complex multiplication

The elliptic curves in class 187425bi do not have complex multiplication.

Modular form 187425.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{8} - 2 q^{13} - q^{16} + q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.