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Properties

Label 363090.b
Number of curves $2$
Conductor $363090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 363090.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363090.b1 363090b2 \([1, 1, 0, -1348848, 584975952]\) \(2306880043867559161/76058277750000\) \(8948180319009750000\) \([2]\) \(12386304\) \(2.4097\)  
363090.b2 363090b1 \([1, 1, 0, 27072, 31580928]\) \(18649681956359/3670404192000\) \(-431819382784608000\) \([2]\) \(6193152\) \(2.0631\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 363090.b have rank \(1\).

Complex multiplication

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

Modular form 363090.2.a.b

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