Properties

Label 6930.t
Number of curves $4$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 6930.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.t1 6930z4 \([1, -1, 1, -85838, 9686567]\) \(95946737295893401/168104301750\) \(122548035975750\) \([2]\) \(49152\) \(1.5967\)  
6930.t2 6930z3 \([1, -1, 1, -69458, -6987769]\) \(50834334659676121/338378906250\) \(246678222656250\) \([2]\) \(49152\) \(1.5967\)  
6930.t3 6930z2 \([1, -1, 1, -7088, 47567]\) \(54014438633401/30015562500\) \(21881345062500\) \([2, 2]\) \(24576\) \(1.2501\)  
6930.t4 6930z1 \([1, -1, 1, 1732, 5231]\) \(788632918919/475398000\) \(-346565142000\) \([2]\) \(12288\) \(0.90353\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 6930.t do not have complex multiplication.

Modular form 6930.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + q^{11} - 6 q^{13} - q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.