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Properties

Label 439824gb
Number of curves $2$
Conductor $439824$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gb1")
 
E.isogeny_class()
 

Elliptic curves in class 439824gb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
439824.gb1 439824gb1 \([0, 1, 0, -708752, 227610900]\) \(81706955619457/744505344\) \(358769906549784576\) \([2]\) \(7741440\) \(2.1907\) \(\Gamma_0(N)\)-optimal
439824.gb2 439824gb2 \([0, 1, 0, -206992, 544121108]\) \(-2035346265217/264305213568\) \(-127366119715068444672\) \([2]\) \(15482880\) \(2.5372\)  

Rank

sage: E.rank()
 

The elliptic curves in class 439824gb have rank \(0\).

Complex multiplication

The elliptic curves in class 439824gb do not have complex multiplication.

Modular form 439824.2.a.gb

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{9} + q^{11} + 4 q^{13} + 2 q^{15} + q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.