Properties

Label 289800.l
Number of curves $4$
Conductor $289800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 289800.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.l1 289800l4 \([0, 0, 0, -21891657675, 1093451708915750]\) \(49737293673675178002921218/6641736806881023047235\) \(154938436230920505645898080000000\) \([2]\) \(849346560\) \(4.9044\)  
289800.l2 289800l2 \([0, 0, 0, -21135342675, 1182643180550750]\) \(89516703758060574923008036/1985322833430374025\) \(23156805529131882627600000000\) \([2, 2]\) \(424673280\) \(4.5578\)  
289800.l3 289800l1 \([0, 0, 0, -21135230175, 1182656400313250]\) \(358061097267989271289240144/176126855625\) \(513585911002500000000\) \([2]\) \(212336640\) \(4.2112\) \(\Gamma_0(N)\)-optimal
289800.l4 289800l3 \([0, 0, 0, -20380827675, 1270988587385750]\) \(-40133926989810174413190818/6689384645060302103835\) \(-156049964999966727478262880000000\) \([2]\) \(849346560\) \(4.9044\)  

Rank

sage: E.rank()
 

The elliptic curves in class 289800.l have rank \(1\).

Complex multiplication

The elliptic curves in class 289800.l do not have complex multiplication.

Modular form 289800.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{7} - 4 q^{11} + 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.