Properties

Label 26010o
Number of curves $4$
Conductor $26010$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 26010o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26010.n3 26010o1 \([1, -1, 0, -262755, -45204075]\) \(114013572049/15667200\) \(275684560235827200\) \([2]\) \(442368\) \(2.0733\) \(\Gamma_0(N)\)-optimal
26010.n2 26010o2 \([1, -1, 0, -1095075, 395759061]\) \(8253429989329/936360000\) \(16476460045344360000\) \([2, 2]\) \(884736\) \(2.4199\)  
26010.n4 26010o3 \([1, -1, 0, 1505925, 1989131661]\) \(21464092074671/109596256200\) \(-1928487266007330616200\) \([2]\) \(1769472\) \(2.7664\)  
26010.n1 26010o4 \([1, -1, 0, -17013195, 27014039325]\) \(30949975477232209/478125000\) \(8413225104853125000\) \([2]\) \(1769472\) \(2.7664\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26010o have rank \(0\).

Complex multiplication

The elliptic curves in class 26010o do not have complex multiplication.

Modular form 26010.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.