Properties

Label 116380.a
Number of curves $4$
Conductor $116380$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116380.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116380.a1 116380e4 \([0, 1, 0, -3756076, 2800628724]\) \(154639330142416/33275\) \(1261028916857600\) \([2]\) \(2566080\) \(2.2822\)  
116380.a2 116380e3 \([0, 1, 0, -235581, 43377040]\) \(610462990336/8857805\) \(20980368604218320\) \([2]\) \(1283040\) \(1.9356\)  
116380.a3 116380e2 \([0, 1, 0, -53076, 2641924]\) \(436334416/171875\) \(6513579116000000\) \([2]\) \(855360\) \(1.7329\)  
116380.a4 116380e1 \([0, 1, 0, -23981, -1408100]\) \(643956736/15125\) \(35824685138000\) \([2]\) \(427680\) \(1.3863\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116380.a have rank \(0\).

Complex multiplication

The elliptic curves in class 116380.a do not have complex multiplication.

Modular form 116380.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.