Properties

Label 270480ch
Number of curves $2$
Conductor $270480$
CM no
Rank $1$
Graph

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

Elliptic curves in class 270480ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.ch1 270480ch1 \([0, -1, 0, -192096, 31000320]\) \(1626794704081/83462400\) \(40219721308569600\) \([2]\) \(3538944\) \(1.9440\) \(\Gamma_0(N)\)-optimal
270480.ch2 270480ch2 \([0, -1, 0, 121504, 122069760]\) \(411664745519/13605414480\) \(-6556317319813201920\) \([2]\) \(7077888\) \(2.2906\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480ch have rank \(1\).

Complex multiplication

The elliptic curves in class 270480ch do not have complex multiplication.

Modular form 270480.2.a.ch

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