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Properties

Label 1554n
Number of curves $3$
Conductor $1554$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 1554n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1554.l2 1554n1 \([1, 0, 0, -4767, 127449]\) \(-11980221891814513/127896039936\) \(-127896039936\) \([9]\) \(3888\) \(0.94763\) \(\Gamma_0(N)\)-optimal
1554.l3 1554n2 \([1, 0, 0, 15753, 666801]\) \(432326451325256207/441510751160136\) \(-441510751160136\) \([3]\) \(11664\) \(1.4969\)  
1554.l1 1554n3 \([1, 0, 0, -159177, -34893381]\) \(-446030778735169043473/267461260498268466\) \(-267461260498268466\) \([]\) \(34992\) \(2.0462\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1554n have rank \(1\).

Complex multiplication

The elliptic curves in class 1554n do not have complex multiplication.

Modular form 1554.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 3 q^{10} - 6 q^{11} + q^{12} - 4 q^{13} + q^{14} - 3 q^{15} + q^{16} + q^{18} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.