Properties

Label 30960.bc
Number of curves $4$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30960.bc1 30960cd4 [0, 0, 0, -120747, 16039514] [4] 147456  
30960.bc2 30960cd2 [0, 0, 0, -12747, -138886] [2, 2] 73728  
30960.bc3 30960cd1 [0, 0, 0, -9867, -376774] [2] 36864 \(\Gamma_0(N)\)-optimal
30960.bc4 30960cd3 [0, 0, 0, 49173, -1092454] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 30960.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 30960.bc do not have complex multiplication.

Modular form 30960.2.a.bc

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.