Properties

Label 22800.h
Number of curves $2$
Conductor $22800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 22800.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22800.h1 22800cl2 \([0, -1, 0, -27208, 2812912]\) \(-1392225385/1316928\) \(-2107084800000000\) \([]\) \(103680\) \(1.6367\)  
22800.h2 22800cl1 \([0, -1, 0, 2792, -67088]\) \(1503815/2052\) \(-3283200000000\) \([]\) \(34560\) \(1.0874\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22800.h have rank \(1\).

Complex multiplication

The elliptic curves in class 22800.h do not have complex multiplication.

Modular form 22800.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 3 q^{11} + 2 q^{13} + 6 q^{17} - q^{19} + O(q^{20})\) 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.