Properties

Label 14450bc
Number of curves $2$
Conductor $14450$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 14450bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14450.q2 14450bc1 \([1, -1, 1, -3480, 117147]\) \(-60698457/40960\) \(-3144320000000\) \([]\) \(59904\) \(1.0986\) \(\Gamma_0(N)\)-optimal
14450.q1 14450bc2 \([1, -1, 1, -3152730, -2153969853]\) \(-45145776875761017/2441406250\) \(-187416076660156250\) \([]\) \(778752\) \(2.3811\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14450bc have rank \(2\).

Complex multiplication

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

Modular form 14450.2.a.bc

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.