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Properties

Label 72450.bc
Number of curves $2$
Conductor $72450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 72450.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.bc1 72450bi2 \([1, -1, 0, -56309517, -162615416859]\) \(1733490909744055732873/99355964553216\) \(1131726533738976000000\) \([2]\) \(8650752\) \(3.1035\)  
72450.bc2 72450bi1 \([1, -1, 0, -3317517, -2844536859]\) \(-354499561600764553/101902222098432\) \(-1160729998589952000000\) \([2]\) \(4325376\) \(2.7569\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 72450.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 72450.bc do not have complex multiplication.

Modular form 72450.2.a.bc

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