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Properties

Label 33150.j
Number of curves $2$
Conductor $33150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 33150.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.j1 33150e1 \([1, 1, 0, -542375, 154003125]\) \(-1129285954562528881/4130500608000\) \(-64539072000000000\) \([]\) \(622080\) \(2.0863\) \(\Gamma_0(N)\)-optimal
33150.j2 33150e2 \([1, 1, 0, 1197625, 806743125]\) \(12158099101398341519/25007954601383520\) \(-390749290646617500000\) \([]\) \(1866240\) \(2.6356\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33150.j have rank \(0\).

Complex multiplication

The elliptic curves in class 33150.j do not have complex multiplication.

Modular form 33150.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} + q^{9} - 3 q^{11} - q^{12} - q^{13} - 4 q^{14} + q^{16} + q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.