Properties

Label 78400.ce
Number of curves $2$
Conductor $78400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 78400.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.ce1 78400iq2 \([0, 1, 0, -38496033, -91949611937]\) \(-5452947409/250\) \(-289254654976000000000\) \([]\) \(5806080\) \(3.0018\)  
78400.ce2 78400iq1 \([0, 1, 0, -80033, -327451937]\) \(-49/40\) \(-46280744796160000000\) \([]\) \(1935360\) \(2.4525\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 78400.ce have rank \(1\).

Complex multiplication

The elliptic curves in class 78400.ce do not have complex multiplication.

Modular form 78400.2.a.ce

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{9} + 3 q^{11} - 5 q^{13} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.