Properties

Label 161448bj
Number of curves $4$
Conductor $161448$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 161448bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161448.n3 161448bj1 \([0, -1, 0, -7047, 228540]\) \(2725888/21\) \(298201236816\) \([2]\) \(230400\) \(1.0308\) \(\Gamma_0(N)\)-optimal
161448.n2 161448bj2 \([0, -1, 0, -11852, -117420]\) \(810448/441\) \(100195615570176\) \([2, 2]\) \(460800\) \(1.3774\)  
161448.n4 161448bj3 \([0, -1, 0, 45808, -970788]\) \(11696828/7203\) \(-6546113550584832\) \([2]\) \(921600\) \(1.7240\)  
161448.n1 161448bj4 \([0, -1, 0, -146392, -21482372]\) \(381775972/567\) \(515291737218048\) \([2]\) \(921600\) \(1.7240\)  

Rank

sage: E.rank()
 

The elliptic curves in class 161448bj have rank \(0\).

Complex multiplication

The elliptic curves in class 161448bj do not have complex multiplication.

Modular form 161448.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 2 q^{13} - 2 q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.