Properties

Label 95874.b
Number of curves $4$
Conductor $95874$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 95874.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95874.b1 95874a3 \([1, 1, 0, -359965, -83275799]\) \(8671983378625/82308\) \(48958717904868\) \([2]\) \(870912\) \(1.7892\)  
95874.b2 95874a4 \([1, 1, 0, -351555, -87341193]\) \(-8078253774625/846825858\) \(-503711769164234418\) \([2]\) \(1741824\) \(2.1357\)  
95874.b3 95874a1 \([1, 1, 0, -6745, 13477]\) \(57066625/32832\) \(19529239275072\) \([2]\) \(290304\) \(1.2398\) \(\Gamma_0(N)\)-optimal
95874.b4 95874a2 \([1, 1, 0, 26895, 141309]\) \(3616805375/2105352\) \(-1252312468513992\) \([2]\) \(580608\) \(1.5864\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95874.b have rank \(1\).

Complex multiplication

The elliptic curves in class 95874.b do not have complex multiplication.

Modular form 95874.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{12} - 4 q^{13} + 4 q^{14} + q^{16} - 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.