Properties

Label 235950.ia
Number of curves $6$
Conductor $235950$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235950.ia1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235950.ia

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235950.ia1 235950ia5 [1, 0, 0, -27270438, 54811063242] [2] 15728640  
235950.ia2 235950ia4 [1, 0, 0, -2556188, -1572002508] [2] 7864320  
235950.ia3 235950ia3 [1, 0, 0, -1709188, 851264492] [2, 2] 7864320  
235950.ia4 235950ia6 [1, 0, 0, -347938, 2170315742] [2] 15728640  
235950.ia5 235950ia2 [1, 0, 0, -196688, -12373008] [2, 2] 3932160  
235950.ia6 235950ia1 [1, 0, 0, 45312, -1483008] [2] 1966080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235950.ia have rank \(1\).

Modular form 235950.2.a.ia

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + q^{13} + q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.