Properties

Label 121275dp
Number of curves $2$
Conductor $121275$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121275dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121275.a2 121275dp1 [0, 0, 1, -98567175, 441097174656] [] 55296000 \(\Gamma_0(N)\)-optimal
121275.a1 121275dp2 [0, 0, 1, -295363425, -36938069991594] [] 276480000  

Rank

sage: E.rank()
 

The elliptic curves in class 121275dp have rank \(1\).

Complex multiplication

The elliptic curves in class 121275dp do not have complex multiplication.

Modular form 121275.2.a.dp

sage: E.q_eigenform(10)
 
\( q - 2q^{2} + 2q^{4} - q^{11} - 6q^{13} - 4q^{16} + 7q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.