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Properties

Label 42042.ch
Number of curves $2$
Conductor $42042$
CM no
Rank $0$
Graph

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

Elliptic curves in class 42042.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42042.ch1 42042bw2 \([1, 1, 1, -114538040, -471735414151]\) \(28826282175168869972161/9077387406557184\) \(52329331998708260880384\) \([]\) \(7836864\) \(3.3349\)  
42042.ch2 42042bw1 \([1, 1, 1, -3553530, 2576825523]\) \(860833894093732321/8282804244\) \(47748718188615444\) \([]\) \(1119552\) \(2.3619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42042.ch have rank \(0\).

Complex multiplication

The elliptic curves in class 42042.ch do not have complex multiplication.

Modular form 42042.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + q^{13} - q^{15} + q^{16} + 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.