Properties

Label 72128cd
Number of curves $2$
Conductor $72128$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72128cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72128.n2 72128cd1 \([0, 1, 0, 108127, 64410079]\) \(4533086375/60669952\) \(-1871120743228506112\) \([2]\) \(1032192\) \(2.1869\) \(\Gamma_0(N)\)-optimal
72128.n1 72128cd2 \([0, 1, 0, -1898913, 942289375]\) \(24553362849625/1755162752\) \(54130938376368422912\) \([2]\) \(2064384\) \(2.5334\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72128cd have rank \(0\).

Complex multiplication

The elliptic curves in class 72128cd do not have complex multiplication.

Modular form 72128.2.a.cd

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{9} + 4q^{11} - 6q^{17} + 6q^{19} + O(q^{20})\)  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.