Properties

Label 344760.cl
Number of curves $4$
Conductor $344760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 344760.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.cl1 344760cl4 \([0, 1, 0, -5525680, -5001293920]\) \(1887517194957938/21849165\) \(215985656349665280\) \([2]\) \(8257536\) \(2.4773\)  
344760.cl2 344760cl2 \([0, 1, 0, -354280, -73984000]\) \(994958062276/98903025\) \(488843275465958400\) \([2, 2]\) \(4128768\) \(2.1308\)  
344760.cl3 344760cl1 \([0, 1, 0, -80500, 7492928]\) \(46689225424/7249905\) \(8958440116005120\) \([4]\) \(2064384\) \(1.7842\) \(\Gamma_0(N)\)-optimal
344760.cl4 344760cl3 \([0, 1, 0, 436640, -356816992]\) \(931329171502/6107473125\) \(-60374233593872640000\) \([2]\) \(8257536\) \(2.4773\)  

Rank

sage: E.rank()
 

The elliptic curves in class 344760.cl have rank \(1\).

Complex multiplication

The elliptic curves in class 344760.cl do not have complex multiplication.

Modular form 344760.2.a.cl

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 4 q^{11} + q^{15} + q^{17} - 8 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.