Properties

Label 79560.e
Number of curves $2$
Conductor $79560$
CM no
Rank $1$
Graph

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

Elliptic curves in class 79560.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.e1 79560l1 \([0, 0, 0, -879303, 307864442]\) \(402876451435348816/13746755117745\) \(2565474427094042880\) \([2]\) \(1474560\) \(2.3044\) \(\Gamma_0(N)\)-optimal
79560.e2 79560l2 \([0, 0, 0, 301677, 1073375678]\) \(4067455675907516/669098843633025\) \(-499479610376678630400\) \([2]\) \(2949120\) \(2.6510\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79560.e have rank \(1\).

Complex multiplication

The elliptic curves in class 79560.e do not have complex multiplication.

Modular form 79560.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 4 q^{11} + q^{13} - q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.