Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.e1 23520bh4 \([0, -1, 0, -4116016, -3212760284]\) \(128025588102048008/7875\) \(474360768000\) \([2]\) \(294912\) \(2.1489\)  
23520.e2 23520bh3 \([0, -1, 0, -288136, -37311560]\) \(43919722445768/15380859375\) \(926485875000000000\) \([2]\) \(294912\) \(2.1489\)  
23520.e3 23520bh1 \([0, -1, 0, -257266, -50128784]\) \(250094631024064/62015625\) \(466948881000000\) \([2, 2]\) \(147456\) \(1.8023\) \(\Gamma_0(N)\)-optimal
23520.e4 23520bh2 \([0, -1, 0, -226641, -62544159]\) \(-2671731885376/1969120125\) \(-948899895648768000\) \([2]\) \(294912\) \(2.1489\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.