Properties

Label 6930c
Number of curves 2
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.i1 6930c1 [1, -1, 0, -2094, -33580] [2] 7680 \(\Gamma_0(N)\)-optimal
6930.i2 6930c2 [1, -1, 0, 2226, -157132] [2] 15360  

Rank

sage: E.rank()
 

The elliptic curves in class 6930c have rank \(0\).

Modular form 6930.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.