Properties

Label 83790.ft
Number of curves $4$
Conductor $83790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ft1")
 
E.isogeny_class()
 

Elliptic curves in class 83790.ft

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.ft1 83790fs4 \([1, -1, 1, -426677, -107146119]\) \(100162392144121/23457780\) \(2011882797871380\) \([2]\) \(1179648\) \(1.9269\)  
83790.ft2 83790fs3 \([1, -1, 1, -197357, 32866089]\) \(9912050027641/311647500\) \(26728797194347500\) \([2]\) \(1179648\) \(1.9269\)  
83790.ft3 83790fs2 \([1, -1, 1, -29777, -1253199]\) \(34043726521/11696400\) \(1003154857664400\) \([2, 2]\) \(589824\) \(1.5804\)  
83790.ft4 83790fs1 \([1, -1, 1, 5503, -138351]\) \(214921799/218880\) \(-18772488564480\) \([2]\) \(294912\) \(1.2338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 83790.ft have rank \(0\).

Complex multiplication

The elliptic curves in class 83790.ft do not have complex multiplication.

Modular form 83790.2.a.ft

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4 q^{11} + 6 q^{13} + q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) 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 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.