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Properties

Label 1150f
Number of curves $2$
Conductor $1150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1150f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1150.i2 1150f1 \([1, 1, 1, -38, -89]\) \(243135625/48668\) \(1216700\) \([]\) \(144\) \(-0.11627\) \(\Gamma_0(N)\)-optimal
1150.i1 1150f2 \([1, 1, 1, -2913, -61729]\) \(109348914285625/1472\) \(36800\) \([]\) \(432\) \(0.43304\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1150f have rank \(0\).

Complex multiplication

The elliptic curves in class 1150f do not have complex multiplication.

Modular form 1150.2.a.f

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