Properties

Label 15210.bc
Number of curves $2$
Conductor $15210$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 15210.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bc1 15210bh2 \([1, -1, 1, -69998, 6403011]\) \(10779215329/1232010\) \(4335127500989610\) \([2]\) \(129024\) \(1.7327\)  
15210.bc2 15210bh1 \([1, -1, 1, 6052, 501531]\) \(6967871/35100\) \(-123507906011100\) \([2]\) \(64512\) \(1.3862\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15210.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 15210.bc do not have complex multiplication.

Modular form 15210.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} + 4 q^{11} - 2 q^{14} + q^{16} - 8 q^{17} + 6 q^{19} + O(q^{20})\) 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 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.