Properties

Label 369600.hb
Number of curves $2$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.hb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.hb1 369600hb1 \([0, -1, 0, -224533, -84648563]\) \(-4890195460096/9282994875\) \(-2376446688000000000\) \([]\) \(5971968\) \(2.2158\) \(\Gamma_0(N)\)-optimal
369600.hb2 369600hb2 \([0, -1, 0, 1935467, 1794551437]\) \(3132137615458304/7250937873795\) \(-1856240095691520000000\) \([]\) \(17915904\) \(2.7651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.hb have rank \(1\).

Complex multiplication

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

Modular form 369600.2.a.hb

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