↑

Properties

Label 40425.v
Number of curves $2$
Conductor $40425$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 40425.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.v1 40425cj2 \([1, 0, 0, -89013, 6306642]\) \(14553591673375/5208653241\) \(27915125963484375\) \([2]\) \(368640\) \(1.8565\)  
40425.v2 40425cj1 \([1, 0, 0, 16862, 695267]\) \(98931640625/96059601\) \(-514819424109375\) \([2]\) \(184320\) \(1.5100\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40425.v have rank \(1\).

Complex multiplication

The elliptic curves in class 40425.v do not have complex multiplication.

Modular form 40425.2.a.v

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