Properties

Label 291018.bp
Number of curves $2$
Conductor $291018$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 291018.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
291018.bp1 291018bp2 \([1, 0, 1, -1741369582, -27965354262688]\) \(120986373702456846135875233/21429653098766238144\) \(103436842444002767169602496\) \([]\) \(219469824\) \(3.9964\)  
291018.bp2 291018bp1 \([1, 0, 1, -51964462, 91207788128]\) \(3215014175651328584353/1115930860975816704\) \(5386385123135820849217536\) \([]\) \(73156608\) \(3.4471\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 291018.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 291018.bp do not have complex multiplication.

Modular form 291018.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{10} + 3 q^{11} + q^{12} + q^{14} + 3 q^{15} + q^{16} + 3 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.