Properties

Label 309442e
Number of curves $2$
Conductor $309442$
CM no
Rank $0$
Graph

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

Elliptic curves in class 309442e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309442.e2 309442e1 \([1, -1, 0, 427253693, 1724674077909]\) \(9718763732247834696375/7072327531706974208\) \(-6276716717627583822972059648\) \([2]\) \(145981440\) \(4.0222\) \(\Gamma_0(N)\)-optimal
309442.e1 309442e2 \([1, -1, 0, -1936960067, 14628079937237]\) \(905556497427272537015625/419898849662109966848\) \(372661774722788201804387967488\) \([2]\) \(291962880\) \(4.3688\)  

Rank

sage: E.rank()
 

The elliptic curves in class 309442e have rank \(0\).

Complex multiplication

The elliptic curves in class 309442e do not have complex multiplication.

Modular form 309442.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} + 2 q^{11} + 2 q^{13} + q^{14} + q^{16} - 2 q^{17} + 3 q^{18} + 6 q^{19} + O(q^{20})\) 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 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.