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Properties

Label 141610ch
Number of curves $2$
Conductor $141610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 141610ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.t2 141610ch1 \([1, -1, 0, -419155, 397954101]\) \(-14090073029577/110146355200\) \(-63665643771389542400\) \([2]\) \(3870720\) \(2.4829\) \(\Gamma_0(N)\)-optimal
141610.t1 141610ch2 \([1, -1, 0, -11081555, 14167377461]\) \(260369943483538377/723136637440\) \(417979872994431265280\) \([2]\) \(7741440\) \(2.8295\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141610ch have rank \(0\).

Complex multiplication

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

Modular form 141610.2.a.ch

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.