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Properties

Label 462550.bc
Number of curves $2$
Conductor $462550$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462550.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 462550.bc do not have complex multiplication.

Modular form 462550.2.a.bc

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

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 462550.bc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462550.bc1 462550bc1 \([1, 0, 1, -578626, 172817428]\) \(-1440749475625/34339712\) \(-510651538350588800\) \([]\) \(7620480\) \(2.1840\) \(\Gamma_0(N)\)-optimal
462550.bc2 462550bc2 \([1, 0, 1, 2469999, 744495588]\) \(112069207574375/80947970048\) \(-1203743509303997235200\) \([]\) \(22861440\) \(2.7333\)