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Properties

Label 73926c
Number of curves $3$
Conductor $73926$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 73926c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73926.j3 73926c1 \([1, -1, 0, 1797, -21027]\) \(9261/8\) \(-554196904344\) \([]\) \(103680\) \(0.94095\) \(\Gamma_0(N)\)-optimal
73926.j2 73926c2 \([1, -1, 0, -18738, 1313748]\) \(-1167051/512\) \(-319217416902144\) \([]\) \(311040\) \(1.4903\)  
73926.j1 73926c3 \([1, -1, 0, -39273, -3024613]\) \(-132651/2\) \(-101002385816694\) \([]\) \(311040\) \(1.4903\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73926c have rank \(1\).

Complex multiplication

The elliptic curves in class 73926c do not have complex multiplication.

Modular form 73926.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{7} - q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} + q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.