Properties

Label 123840.b
Number of curves $2$
Conductor $123840$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 123840.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
123840.b1 123840cj2 [0, 0, 0, -95486988, 359139964912] [2] 15482880  
123840.b2 123840cj1 [0, 0, 0, -5907468, 5730842608] [2] 7741440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 123840.b have rank \(1\).

Complex multiplication

The elliptic curves in class 123840.b do not have complex multiplication.

Modular form 123840.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 4q^{11} - 4q^{13} - 4q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.