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Properties

Label 402522.g
Number of curves $3$
Conductor $402522$
CM no
Rank $1$
Graph

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

Elliptic curves in class 402522.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
402522.g1 402522g1 \([1, 0, 0, -5219582832, 145144621322496]\) \(-15726464326139854896588126629981953/18589878855962488278614016\) \(-18589878855962488278614016\) \([9]\) \(446497920\) \(4.1312\) \(\Gamma_0(N)\)-optimal
402522.g2 402522g2 \([1, 0, 0, -3907616112, 219814537584384]\) \(-6598715236063046891482569127333633/17054923060954328039584062230016\) \(-17054923060954328039584062230016\) \([3]\) \(1339493760\) \(4.6805\)  
402522.g3 402522g3 \([1, 0, 0, 34044882408, -4946617268171784]\) \(4363944588641887373508182221622940287/13096060697351426729216028020563896\) \(-13096060697351426729216028020563896\) \([]\) \(4018481280\) \(5.2298\)  

Rank

sage: E.rank()
 

The elliptic curves in class 402522.g have rank \(1\).

Complex multiplication

The elliptic curves in class 402522.g do not have complex multiplication.

Modular form 402522.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.