Properties

Label 369600se
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("se1")
 
E.isogeny_class()
 

Elliptic curves in class 369600se

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.se1 369600se1 \([0, 1, 0, -12033, -503937]\) \(188183524/3465\) \(3548160000000\) \([2]\) \(884736\) \(1.2027\) \(\Gamma_0(N)\)-optimal
369600.se2 369600se2 \([0, 1, 0, -33, -1451937]\) \(-2/444675\) \(-910694400000000\) \([2]\) \(1769472\) \(1.5493\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600se have rank \(0\).

Complex multiplication

The elliptic curves in class 369600se do not have complex multiplication.

Modular form 369600.2.a.se

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} - 8 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.