↑

Properties

Label 230450q
Number of curves $2$
Conductor $230450$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 230450q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230450.q2 230450q1 \([1, -1, 0, -24172042, 45716064116]\) \(99964020929586731506161/81651246490000000\) \(1275800726406250000000\) \([]\) \(34075776\) \(2.9788\) \(\Gamma_0(N)\)-optimal
230450.q1 230450q2 \([1, -1, 0, -2342545792, -43638859389634]\) \(90984613355465878035683930961/249396782289047639290\) \(3896824723266369363906250\) \([]\) \(238530432\) \(3.9518\)  

Rank

sage: E.rank()
 

The elliptic curves in class 230450q have rank \(0\).

Complex multiplication

The elliptic curves in class 230450q do not have complex multiplication.

Modular form 230450.2.a.q

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.