Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.i1 23520bb4 \([0, -1, 0, -23536, 1397656]\) \(23937672968/45\) \(2710632960\) \([2]\) \(36864\) \(1.0653\)  
23520.i2 23520bb3 \([0, -1, 0, -3936, -65484]\) \(111980168/32805\) \(1976051427840\) \([2]\) \(36864\) \(1.0653\)  
23520.i3 23520bb1 \([0, -1, 0, -1486, 21736]\) \(48228544/2025\) \(15247310400\) \([2, 2]\) \(18432\) \(0.71870\) \(\Gamma_0(N)\)-optimal
23520.i4 23520bb2 \([0, -1, 0, 719, 78625]\) \(85184/5625\) \(-2710632960000\) \([2]\) \(36864\) \(1.0653\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23520.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 2q^{13} + q^{15} + 6q^{17} + O(q^{20})\)  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.