↑

Properties

Label 444925l
Number of curves $2$
Conductor $444925$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 444925l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444925.l2 444925l1 \([0, 1, 1, -114083, 13739119]\) \(163840/13\) \(13029079420703125\) \([]\) \(3110400\) \(1.8358\) \(\Gamma_0(N)\)-optimal
444925.l1 444925l2 \([0, 1, 1, -1825333, -947127756]\) \(671088640/2197\) \(2201914422098828125\) \([]\) \(9331200\) \(2.3851\)  

Rank

sage: E.rank()
 

The elliptic curves in class 444925l have rank \(0\).

Complex multiplication

The elliptic curves in class 444925l do not have complex multiplication.

Modular form 444925.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 4 q^{7} - 2 q^{9} - 6 q^{11} - 2 q^{12} - q^{13} + 4 q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.