Properties

Label 60984w
Number of curves $2$
Conductor $60984$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.h2 60984w1 \([0, 0, 0, -13431, -1003574]\) \(-810448/847\) \(-280031582654208\) \([2]\) \(184320\) \(1.4674\) \(\Gamma_0(N)\)-optimal
60984.h1 60984w2 \([0, 0, 0, -253011, -48967490]\) \(1354435492/539\) \(712807664937984\) \([2]\) \(368640\) \(1.8140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60984w have rank \(1\).

Complex multiplication

The elliptic curves in class 60984w do not have complex multiplication.

Modular form 60984.2.a.w

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{7} - 4q^{13} + 4q^{19} + O(q^{20})\)  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.