Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.o1 23520j4 \([0, -1, 0, -3213240, 2217954600]\) \(60910917333827912/3255076125\) \(196073702927424000\) \([2]\) \(442368\) \(2.3855\)  
23520.o2 23520j3 \([0, -1, 0, -1038865, -379651775]\) \(257307998572864/19456203375\) \(9375755759064576000\) \([2]\) \(442368\) \(2.3855\)  
23520.o3 23520j1 \([0, -1, 0, -211990, 30643600]\) \(139927692143296/27348890625\) \(205924456521000000\) \([2, 2]\) \(221184\) \(2.0389\) \(\Gamma_0(N)\)-optimal
23520.o4 23520j2 \([0, -1, 0, 436280, 180782932]\) \(152461584507448/322998046875\) \(-19456203375000000000\) \([2]\) \(442368\) \(2.3855\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4q^{11} - 2q^{13} - q^{15} + 2q^{17} + O(q^{20})\)  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.