Properties

Label 27930.r
Number of curves $2$
Conductor $27930$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 27930.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.r1 27930p1 \([1, 1, 0, -519327, -253556001]\) \(-131661708271504489/159475479581250\) \(-18762130697254481250\) \([]\) \(967680\) \(2.3919\) \(\Gamma_0(N)\)-optimal
27930.r2 27930p2 \([1, 1, 0, 4382388, 4758786936]\) \(79116632600119361351/128876220703125000\) \(-15162158489501953125000\) \([]\) \(2903040\) \(2.9412\)  

Rank

sage: E.rank()
 

The elliptic curves in class 27930.r have rank \(1\).

Complex multiplication

The elliptic curves in class 27930.r do not have complex multiplication.

Modular form 27930.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 3 q^{11} - q^{12} - 5 q^{13} - q^{15} + q^{16} - 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.