Properties

Label 369600.u
Number of curves $2$
Conductor $369600$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.u1 369600u2 \([0, -1, 0, -1793, -22143]\) \(77860436/17787\) \(145711104000\) \([2]\) \(294912\) \(0.85456\)  
369600.u2 369600u1 \([0, -1, 0, -593, 5457]\) \(11279504/693\) \(1419264000\) \([2]\) \(147456\) \(0.50799\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.u have rank \(2\).

Complex multiplication

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

Modular form 369600.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.