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Properties

Label 16575.h
Number of curves $2$
Conductor $16575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 16575.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16575.h1 16575c1 \([1, 1, 0, -500, -4125]\) \(887503681/89505\) \(1398515625\) \([2]\) \(7680\) \(0.49098\) \(\Gamma_0(N)\)-optimal
16575.h2 16575c2 \([1, 1, 0, 625, -18750]\) \(1723683599/10989225\) \(-171706640625\) \([2]\) \(15360\) \(0.83755\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16575.h have rank \(1\).

Complex multiplication

The elliptic curves in class 16575.h do not have complex multiplication.

Modular form 16575.2.a.h

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