Properties

Label 2160.h
Number of curves $2$
Conductor $2160$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2160.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2160.h1 2160m1 \([0, 0, 0, -648, -6372]\) \(-5971968/25\) \(-125971200\) \([]\) \(864\) \(0.40927\) \(\Gamma_0(N)\)-optimal
2160.h2 2160m2 \([0, 0, 0, 1512, -33588]\) \(8429568/15625\) \(-708588000000\) \([]\) \(2592\) \(0.95857\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2160.h have rank \(0\).

Complex multiplication

The elliptic curves in class 2160.h do not have complex multiplication.

Modular form 2160.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 6 q^{11} - q^{13} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.