Properties

Label 340784h
Number of curves $2$
Conductor $340784$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 340784h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340784.h1 340784h1 \([0, -1, 0, -144520, 21822704]\) \(-1732323601/60416\) \(-11642158884847616\) \([]\) \(1944000\) \(1.8557\) \(\Gamma_0(N)\)-optimal
340784.h2 340784h2 \([0, -1, 0, 664120, -1110273296]\) \(168105213359/2859697196\) \(-551063445418187472896\) \([]\) \(9720000\) \(2.6604\)  

Rank

sage: E.rank()
 

The elliptic curves in class 340784h have rank \(1\).

Complex multiplication

The elliptic curves in class 340784h do not have complex multiplication.

Modular form 340784.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 3 q^{7} - 2 q^{9} - 2 q^{11} + 6 q^{13} - q^{15} - 2 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.