Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ew1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 123840ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
123840.dn2 123840ew1 [0, 0, 0, -5907468, -5730842608] [2] 7741440 \(\Gamma_0(N)\)-optimal
123840.dn1 123840ew2 [0, 0, 0, -95486988, -359139964912] [2] 15482880  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 123840.2.a.ew

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 Cremona 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 Cremona labels.