↑

Properties

Label 101430.fg
Number of curves $2$
Conductor $101430$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("fg1")
 
E.isogeny_class()
 

Elliptic curves in class 101430.fg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.fg1 101430fg2 \([1, -1, 1, -325247, -46231]\) \(44365623586201/25674468750\) \(2201999593423218750\) \([2]\) \(1769472\) \(2.2091\)  
101430.fg2 101430fg1 \([1, -1, 1, -223817, -40577659]\) \(14457238157881/49990500\) \(4287491271850500\) \([2]\) \(884736\) \(1.8626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101430.fg have rank \(0\).

Complex multiplication

The elliptic curves in class 101430.fg do not have complex multiplication.

Modular form 101430.2.a.fg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 2 q^{11} + 6 q^{13} + q^{16} - 6 q^{19} + O(q^{20})\) 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.