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Properties

Label 363090.de
Number of curves $2$
Conductor $363090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("de1")
 
E.isogeny_class()
 

Elliptic curves in class 363090.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363090.de1 363090de1 \([1, 0, 1, -2360209, -1395826204]\) \(12359092816971484921/116188800000\) \(13669496131200000\) \([2]\) \(12288000\) \(2.2590\) \(\Gamma_0(N)\)-optimal
363090.de2 363090de2 \([1, 0, 1, -2305329, -1463811548]\) \(-11516856136356002041/1201114687500000\) \(-141309941869687500000\) \([2]\) \(24576000\) \(2.6056\)  

Rank

sage: E.rank()
 

The elliptic curves in class 363090.de have rank \(0\).

Complex multiplication

The elliptic curves in class 363090.de do not have complex multiplication.

Modular form 363090.2.a.de

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} + q^{13} - q^{15} + q^{16} + 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.