Properties

Label 1568.h
Number of curves $2$
Conductor $1568$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1568.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1568.h1 1568c2 \([0, -1, 0, -408, 1940]\) \(125000/49\) \(2951578112\) \([2]\) \(768\) \(0.51575\)  
1568.h2 1568c1 \([0, -1, 0, 82, 176]\) \(8000/7\) \(-52706752\) \([2]\) \(384\) \(0.16918\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1568.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1568.h do not have complex multiplication.

Modular form 1568.2.a.h

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