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Properties

Label 309738f
Number of curves $2$
Conductor $309738$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 309738f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309738.f1 309738f1 \([1, 1, 0, -4456191, -3310450875]\) \(208014519619149697/19859548161024\) \(934309939497303942144\) \([2]\) \(17971200\) \(2.7616\) \(\Gamma_0(N)\)-optimal
309738.f2 309738f2 \([1, 1, 0, 5305249, -15791428059]\) \(351009842940054143/2493610843714848\) \(-117314119013718336941088\) \([2]\) \(35942400\) \(3.1082\)  

Rank

sage: E.rank()
 

The elliptic curves in class 309738f have rank \(0\).

Complex multiplication

The elliptic curves in class 309738f do not have complex multiplication.

Modular form 309738.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} + 2 q^{10} + q^{11} - q^{12} + q^{13} - 2 q^{14} + 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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.