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Properties

Label 301665.l
Number of curves $2$
Conductor $301665$
CM no
Rank $1$
Graph

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

Elliptic curves in class 301665.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.l1 301665l2 \([1, 1, 1, -145211310, 673456830990]\) \(31932643435462896517/15181425\) \(160991411893746525\) \([2]\) \(27316224\) \(3.0745\)  
301665.l2 301665l1 \([1, 1, 1, -9074205, 10523584482]\) \(-7792185873540277/5375525715\) \(-57004759074262876695\) \([2]\) \(13658112\) \(2.7280\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301665.l have rank \(1\).

Complex multiplication

The elliptic curves in class 301665.l do not have complex multiplication.

Modular form 301665.2.a.l

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