Properties

Label 23400be
Number of curves $4$
Conductor $23400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 23400be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23400.w3 23400be1 \([0, 0, 0, -1650, -14875]\) \(2725888/1053\) \(191909250000\) \([2]\) \(16384\) \(0.86400\) \(\Gamma_0(N)\)-optimal
23400.w2 23400be2 \([0, 0, 0, -11775, 481250]\) \(61918288/1521\) \(4435236000000\) \([2, 2]\) \(32768\) \(1.2106\)  
23400.w4 23400be3 \([0, 0, 0, 1725, 1520750]\) \(48668/85683\) \(-999406512000000\) \([2]\) \(65536\) \(1.5571\)  
23400.w1 23400be4 \([0, 0, 0, -187275, 31193750]\) \(62275269892/39\) \(454896000000\) \([2]\) \(65536\) \(1.5571\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23400be have rank \(1\).

Complex multiplication

The elliptic curves in class 23400be do not have complex multiplication.

Modular form 23400.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.