Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("rz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.rz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.rz1 369600rz1 \([0, 1, 0, -3008, -62262]\) \(3010936384/121275\) \(121275000000\) \([2]\) \(540672\) \(0.89295\) \(\Gamma_0(N)\)-optimal
369600.rz2 369600rz2 \([0, 1, 0, 1367, -224137]\) \(4410944/343035\) \(-21954240000000\) \([2]\) \(1081344\) \(1.2395\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.rz

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} - 2 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.