Properties

Label 95370.bi
Number of curves $2$
Conductor $95370$
CM no
Rank $1$
Graph

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

Elliptic curves in class 95370.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.bi1 95370bo1 \([1, 0, 1, -25583, -1334482]\) \(76711450249/12622500\) \(304676464702500\) \([2]\) \(552960\) \(1.5008\) \(\Gamma_0(N)\)-optimal
95370.bi2 95370bo2 \([1, 0, 1, 46667, -7490182]\) \(465664585751/1274620050\) \(-30766229405658450\) \([2]\) \(1105920\) \(1.8473\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95370.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 95370.bi do not have complex multiplication.

Modular form 95370.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 4 q^{13} + 4 q^{14} + q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.