Properties

Label 94136.f
Number of curves $4$
Conductor $94136$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 94136.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94136.f1 94136f4 [0, 0, 0, -502619, 137152790] [2] 563200  
94136.f2 94136f3 [0, 0, 0, -99179, -9511098] [2] 563200  
94136.f3 94136f2 [0, 0, 0, -31939, 2067630] [2, 2] 281600  
94136.f4 94136f1 [0, 0, 0, 1681, 137842] [2] 140800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94136.f have rank \(1\).

Complex multiplication

The elliptic curves in class 94136.f do not have complex multiplication.

Modular form 94136.2.a.f

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.