Properties

Label 26010.b
Number of curves $4$
Conductor $26010$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 26010.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26010.b1 26010c4 \([1, -1, 0, -332115, -73583875]\) \(8527173507/200\) \(95019954125400\) \([2]\) \(221184\) \(1.7941\)  
26010.b2 26010c3 \([1, -1, 0, -19995, -1234459]\) \(-1860867/320\) \(-152031926600640\) \([2]\) \(110592\) \(1.4476\)  
26010.b3 26010c2 \([1, -1, 0, -6990, 60550]\) \(57960603/31250\) \(20366073843750\) \([2]\) \(73728\) \(1.2448\)  
26010.b4 26010c1 \([1, -1, 0, 1680, 6796]\) \(804357/500\) \(-325857181500\) \([2]\) \(36864\) \(0.89824\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26010.b have rank \(1\).

Complex multiplication

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

Modular form 26010.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 2 q^{7} - q^{8} + q^{10} - 6 q^{11} - 4 q^{13} + 2 q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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 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.