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Properties

Label 112530ch
Number of curves $2$
Conductor $112530$
CM no
Rank $1$
Graph

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

Elliptic curves in class 112530ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112530.cc2 112530ch1 \([1, 1, 1, 270735, -239871345]\) \(1238798620042199/14760960000000\) \(-26149941058560000000\) \([2]\) \(3440640\) \(2.4068\) \(\Gamma_0(N)\)-optimal
112530.cc1 112530ch2 \([1, 1, 1, -4530545, -3464410993]\) \(5805223604235668521/435937500000000\) \(772289873437500000000\) \([2]\) \(6881280\) \(2.7533\)  

Rank

sage: E.rank()
 

The elliptic curves in class 112530ch have rank \(1\).

Complex multiplication

The elliptic curves in class 112530ch do not have complex multiplication.

Modular form 112530.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{10} - q^{12} + 4 q^{13} - 2 q^{14} - q^{15} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) 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.