Properties

Label 14450l
Number of curves $4$
Conductor $14450$
CM no
Rank $0$
Graph

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

Elliptic curves in class 14450l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14450.d3 14450l1 \([1, 1, 0, -150, -8450]\) \(-25/2\) \(-30171961250\) \([]\) \(10080\) \(0.69051\) \(\Gamma_0(N)\)-optimal
14450.d1 14450l2 \([1, 1, 0, -36275, -2674475]\) \(-349938025/8\) \(-120687845000\) \([]\) \(30240\) \(1.2398\)  
14450.d2 14450l3 \([1, 1, 0, -21825, 1487125]\) \(-121945/32\) \(-301719612500000\) \([]\) \(50400\) \(1.4952\)  
14450.d4 14450l4 \([1, 1, 0, 158800, -10976000]\) \(46969655/32768\) \(-308960883200000000\) \([]\) \(151200\) \(2.0445\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14450l have rank \(0\).

Complex multiplication

The elliptic curves in class 14450l do not have complex multiplication.

Modular form 14450.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.