Properties

Label 137904y
Number of curves $2$
Conductor $137904$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 137904y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137904.a2 137904y1 \([0, -1, 0, -15760, -1093184]\) \(-48109395853/30081024\) \(-270696487845888\) \([2]\) \(663552\) \(1.4710\) \(\Gamma_0(N)\)-optimal
137904.a1 137904y2 \([0, -1, 0, -282000, -57536064]\) \(275602131611533/53934336\) \(485350343442432\) \([2]\) \(1327104\) \(1.8176\)  

Rank

sage: E.rank()
 

The elliptic curves in class 137904y have rank \(0\).

Complex multiplication

The elliptic curves in class 137904y do not have complex multiplication.

Modular form 137904.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + q^{9} + 2 q^{11} + 4 q^{15} + q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.