Properties

Label 76664.e
Number of curves $2$
Conductor $76664$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76664.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.e1 76664c1 \([0, 0, 0, -23111458, -42765061575]\) \(33256413948450816/2481997\) \(101890003999340368\) \([2]\) \(3348864\) \(2.7132\) \(\Gamma_0(N)\)-optimal
76664.e2 76664c2 \([0, 0, 0, -23063543, -42951211350]\) \(-2065624967846736/17960084863\) \(-11796649994465343223552\) \([2]\) \(6697728\) \(3.0598\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76664.e have rank \(1\).

Complex multiplication

The elliptic curves in class 76664.e do not have complex multiplication.

Modular form 76664.2.a.e

sage: E.q_eigenform(10)
 
\(q + 4q^{5} - q^{7} - 3q^{9} - 4q^{11} + 4q^{13} - 2q^{19} + O(q^{20})\)  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 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.