Properties

Label 15600.bh
Number of curves $2$
Conductor $15600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bh1 15600bu2 \([0, -1, 0, -3639208, 2463436912]\) \(666276475992821/58199166792\) \(465593334336000000000\) \([2]\) \(737280\) \(2.7064\)  
15600.bh2 15600bu1 \([0, -1, 0, -3559208, 2585676912]\) \(623295446073461/5458752\) \(43670016000000000\) \([2]\) \(368640\) \(2.3598\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15600.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 15600.bh do not have complex multiplication.

Modular form 15600.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{7} + q^{9} - 2q^{11} - q^{13} - 4q^{17} - 2q^{19} + O(q^{20})\)  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.