Properties

Label 364650fl
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fl1")
 
E.isogeny_class()
 

Elliptic curves in class 364650fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.fl1 364650fl1 \([1, 0, 0, -75513, -7270983]\) \(3047678972871625/304559880768\) \(4758748137000000\) \([2]\) \(3096576\) \(1.7446\) \(\Gamma_0(N)\)-optimal
364650.fl2 364650fl2 \([1, 0, 0, 93487, -35155983]\) \(5783051584712375/37533175779528\) \(-586455871555125000\) \([2]\) \(6193152\) \(2.0912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 364650fl have rank \(1\).

Complex multiplication

The elliptic curves in class 364650fl do not have complex multiplication.

Modular form 364650.2.a.fl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - q^{13} - 2 q^{14} + q^{16} + q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.