Properties

Label 1152.h
Number of curves $2$
Conductor $1152$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1152.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.h1 1152g1 \([0, 0, 0, -21, 34]\) \(10976\) \(93312\) \([2]\) \(96\) \(-0.30712\) \(\Gamma_0(N)\)-optimal
1152.h2 1152g2 \([0, 0, 0, 24, 160]\) \(128\) \(-11943936\) \([2]\) \(192\) \(0.039450\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1152.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1152.h do not have complex multiplication.

Modular form 1152.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 4q^{7} - 2q^{11} + 2q^{13} + 2q^{17} - 2q^{19} + O(q^{20})\)  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.