Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("rn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.rn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.rn1 369600rn2 \([0, 1, 0, -90656432833, 2818545808546463]\) \(160934676078320454012702173/86430430219822569086976\) \(44252380272549155372531712000000000\) \([2]\) \(3220439040\) \(5.3391\)  
369600.rn2 369600rn1 \([0, 1, 0, 21737807167, 345535345826463]\) \(2218712073897830722499107/1384711926834951880704\) \(-708972506539495362920448000000000\) \([2]\) \(1610219520\) \(4.9925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.rn

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} - 2 q^{13} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.