Properties

Label 141120.ef
Number of curves $8$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.ef1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ef1 141120dz7 [0, 0, 0, -9913186668, 379898903267408] [2] 84934656  
141120.ef2 141120dz6 [0, 0, 0, -619587948, 5935643093072] [2, 2] 42467328  
141120.ef3 141120dz8 [0, 0, 0, -574429548, 6837564721232] [2] 84934656  
141120.ef4 141120dz4 [0, 0, 0, -122986668, 515740787408] [2] 28311552  
141120.ef5 141120dz3 [0, 0, 0, -41560428, 78374627408] [2] 21233664  
141120.ef6 141120dz2 [0, 0, 0, -16299948, -13297319728] [2, 2] 14155776  
141120.ef7 141120dz1 [0, 0, 0, -14042028, -20245391152] [2] 7077888 \(\Gamma_0(N)\)-optimal
141120.ef8 141120dz5 [0, 0, 0, 54260052, -97658855728] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 141120.ef have rank \(0\).

Modular form 141120.2.a.ef

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.