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Properties

Label 9150.e
Number of curves $2$
Conductor $9150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 9150.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9150.e1 9150c2 \([1, 1, 0, -12875, -712125]\) \(-15107691357361/5067577806\) \(-79180903218750\) \([]\) \(42000\) \(1.3789\)  
9150.e2 9150c1 \([1, 1, 0, -125, 4125]\) \(-13997521/474336\) \(-7411500000\) \([]\) \(8400\) \(0.57416\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9150.e have rank \(0\).

Complex multiplication

The elliptic curves in class 9150.e do not have complex multiplication.

Modular form 9150.2.a.e

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.