Properties

Label 138624u
Number of curves $2$
Conductor $138624$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 138624u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138624.y2 138624u1 \([0, 1, 0, 602, 9854]\) \(4000/9\) \(-54196854912\) \([2]\) \(115200\) \(0.74377\) \(\Gamma_0(N)\)-optimal
138624.y1 138624u2 \([0, 1, 0, -4813, 104075]\) \(16000/3\) \(2312399142912\) \([2]\) \(230400\) \(1.0903\)  

Rank

sage: E.rank()
 

The elliptic curves in class 138624u have rank \(1\).

Complex multiplication

The elliptic curves in class 138624u do not have complex multiplication.

Modular form 138624.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} + 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.