Properties

Label 23520.h
Number of curves $4$
Conductor $23520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 23520.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.h1 23520bc4 \([0, -1, 0, -691896, 221748696]\) \(608119035935048/826875\) \(49807880640000\) \([2]\) \(147456\) \(1.9025\)  
23520.h2 23520bc3 \([0, -1, 0, -109776, -9315900]\) \(2428799546888/778248135\) \(46878778795322880\) \([2]\) \(147456\) \(1.9025\)  
23520.h3 23520bc1 \([0, -1, 0, -43626, 3411360]\) \(1219555693504/43758225\) \(329479130433600\) \([2, 2]\) \(73728\) \(1.5559\) \(\Gamma_0(N)\)-optimal
23520.h4 23520bc2 \([0, -1, 0, 16399, 12018945]\) \(1012048064/130203045\) \(-62743584936775680\) \([2]\) \(147456\) \(1.9025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.h have rank \(1\).

Complex multiplication

The elliptic curves in class 23520.h do not have complex multiplication.

Modular form 23520.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.