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Properties

Label 303450.fk
Number of curves $2$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fk1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.fk1 303450fk2 \([1, 1, 1, -24163, -1366219]\) \(20324066489/1411788\) \(108376788187500\) \([2]\) \(1966080\) \(1.4409\)  
303450.fk2 303450fk1 \([1, 1, 1, 1337, -91219]\) \(3442951/49392\) \(-3791607750000\) \([2]\) \(983040\) \(1.0943\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.fk have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.fk do not have complex multiplication.

Modular form 303450.2.a.fk

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