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Properties

Label 87362.g
Number of curves $3$
Conductor $87362$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 87362.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87362.g1 87362q3 \([1, 1, 0, -3735635, -22355849171]\) \(-69173457625/2550136832\) \(-212540256589988350656512\) \([]\) \(6998400\) \(3.1563\)  
87362.g2 87362q1 \([1, 1, 0, -677965, 214647701]\) \(-413493625/152\) \(-12668386494516632\) \([]\) \(777600\) \(2.0577\) \(\Gamma_0(N)\)-optimal
87362.g3 87362q2 \([1, 1, 0, 414060, 816877648]\) \(94196375/3511808\) \(-292690401569312265728\) \([]\) \(2332800\) \(2.6070\)  

Rank

sage: E.rank()
 

The elliptic curves in class 87362.g have rank \(1\).

Complex multiplication

The elliptic curves in class 87362.g do not have complex multiplication.

Modular form 87362.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{12} + 5 q^{13} - q^{14} + q^{16} - 3 q^{17} + 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.