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Properties

Label 247962.l
Number of curves $2$
Conductor $247962$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 247962.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.l1 247962l1 \([1, 1, 0, -11403223, 12687986005]\) \(6793805286030262681/1048227429629952\) \(25301661910385610866688\) \([2]\) \(43352064\) \(3.0222\) \(\Gamma_0(N)\)-optimal
247962.l2 247962l2 \([1, 1, 0, 19855017, 70046856405]\) \(35862531227445945959/108547797844556928\) \(-2620079960271044124028032\) \([2]\) \(86704128\) \(3.3688\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247962.l have rank \(1\).

Complex multiplication

The elliptic curves in class 247962.l do not have complex multiplication.

Modular form 247962.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 4 q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} - 4 q^{10} - q^{11} - q^{12} - q^{13} - 2 q^{14} - 4 q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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.