Properties

Label 121680cu
Number of curves $2$
Conductor $121680$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 121680cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121680.eb2 121680cu1 \([0, 0, 0, 32448, 2917616]\) \(7077888/10985\) \(-5863863973294080\) \([]\) \(580608\) \(1.7109\) \(\Gamma_0(N)\)-optimal
121680.eb1 121680cu2 \([0, 0, 0, -1022112, 399572784]\) \(-303464448/1625\) \(-632360478776832000\) \([]\) \(1741824\) \(2.2602\)  

Rank

sage: E.rank()
 

The elliptic curves in class 121680cu have rank \(1\).

Complex multiplication

The elliptic curves in class 121680cu do not have complex multiplication.

Modular form 121680.2.a.cu

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 3 q^{11} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.