Properties

Label 150075.f
Number of curves $2$
Conductor $150075$
CM no
Rank $0$
Graph

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

Elliptic curves in class 150075.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150075.f1 150075f1 \([1, -1, 1, -9005, -324628]\) \(7088952961/50025\) \(569816015625\) \([2]\) \(393216\) \(1.0884\) \(\Gamma_0(N)\)-optimal
150075.f2 150075f2 \([1, -1, 1, -3380, -729628]\) \(-374805361/20020005\) \(-228040369453125\) \([2]\) \(786432\) \(1.4350\)  

Rank

sage: E.rank()
 

The elliptic curves in class 150075.f have rank \(0\).

Complex multiplication

The elliptic curves in class 150075.f do not have complex multiplication.

Modular form 150075.2.a.f

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.