Properties

Label 6930.be
Number of curves $2$
Conductor $6930$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.be1 6930bf1 \([1, -1, 1, -1517, 19541]\) \(529278808969/88704000\) \(64665216000\) \([2]\) \(7680\) \(0.79544\) \(\Gamma_0(N)\)-optimal
6930.be2 6930bf2 \([1, -1, 1, 2803, 107669]\) \(3342032927351/8893500000\) \(-6483361500000\) \([2]\) \(15360\) \(1.1420\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6930.be have rank \(1\).

Complex multiplication

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

Modular form 6930.2.a.be

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.