Properties

Label 10780e
Number of curves $2$
Conductor $10780$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10780e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10780.e2 10780e1 \([0, -1, 0, 124, -440]\) \(16674224/15125\) \(-189728000\) \([]\) \(3456\) \(0.27576\) \(\Gamma_0(N)\)-optimal
10780.e1 10780e2 \([0, -1, 0, -1276, 24200]\) \(-18330740176/8857805\) \(-111112305920\) \([]\) \(10368\) \(0.82507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10780e have rank \(1\).

Complex multiplication

The elliptic curves in class 10780e do not have complex multiplication.

Modular form 10780.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2q^{9} - q^{11} + 4q^{13} + q^{15} - 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.