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Properties

Label 441525bc
Number of curves $2$
Conductor $441525$
CM no
Rank $0$
Graph

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

Elliptic curves in class 441525bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
441525.bc1 441525bc1 \([1, 0, 0, -378888, 86857767]\) \(5177717/189\) \(219573452478515625\) \([2]\) \(6021120\) \(2.0971\) \(\Gamma_0(N)\)-optimal
441525.bc2 441525bc2 \([1, 0, 0, 146737, 309197142]\) \(300763/35721\) \(-41499382518439453125\) \([2]\) \(12042240\) \(2.4437\)  

Rank

sage: E.rank()
 

The elliptic curves in class 441525bc have rank \(0\).

Complex multiplication

The elliptic curves in class 441525bc do not have complex multiplication.

Modular form 441525.2.a.bc

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