Properties

Label 92400.da
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.da1 92400bp2 \([0, -1, 0, -52491208, -146361229088]\) \(7997484869919944276/116700507\) \(233401014000000000\) \([2]\) \(5713920\) \(2.8845\)  
92400.da2 92400bp1 \([0, -1, 0, -3283708, -2281669088]\) \(7831544736466064/29831377653\) \(14915688826500000000\) \([2]\) \(2856960\) \(2.5379\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.da have rank \(0\).

Complex multiplication

The elliptic curves in class 92400.da do not have complex multiplication.

Modular form 92400.2.a.da

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + q^{11} - 4q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.