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Properties

Label 141610.u
Number of curves $2$
Conductor $141610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 141610.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.u1 141610cb2 \([1, -1, 0, -42259079, 105747604045]\) \(8568561392847/23120\) \(22519757944115174960\) \([2]\) \(14450688\) \(2.9476\)  
141610.u2 141610cb1 \([1, -1, 0, -2608279, 1695974685]\) \(-2014698447/108800\) \(-105975331501718470400\) \([2]\) \(7225344\) \(2.6010\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141610.u have rank \(1\).

Complex multiplication

The elliptic curves in class 141610.u do not have complex multiplication.

Modular form 141610.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - 3 q^{9} - q^{10} - 6 q^{11} + 2 q^{13} + q^{16} + 3 q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.