Properties

Label 377520fk
Number of curves $2$
Conductor $377520$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("fk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 377520fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.fk2 377520fk1 \([0, 1, 0, 7704, -719820]\) \(6967871/35100\) \(-254696616345600\) \([2]\) \(1474560\) \(1.4465\) \(\Gamma_0(N)\)-optimal
377520.fk1 377520fk2 \([0, 1, 0, -89096, -9199500]\) \(10779215329/1232010\) \(8939851233730560\) \([2]\) \(2949120\) \(1.7931\)  

Rank

sage: E.rank()
 

The elliptic curves in class 377520fk have rank \(1\).

Complex multiplication

The elliptic curves in class 377520fk do not have complex multiplication.

Modular form 377520.2.a.fk

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2q^{7} + q^{9} + q^{13} - q^{15} - 8q^{17} - 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.