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Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 363090.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363090.f1 363090f2 \([1, 1, 0, -812788, 676358992]\) \(-210220950826201/578658163200\) \(-163456608735802636800\) \([]\) \(13716864\) \(2.5659\)  
363090.f2 363090f1 \([1, 1, 0, 87587, -21071483]\) \(263059819799/833625000\) \(-235478429447625000\) \([]\) \(4572288\) \(2.0166\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 363090.2.a.f

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.