Properties

Label 9900l
Number of curves $4$
Conductor $9900$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9900l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9900.e4 9900l1 \([0, 0, 0, 49200, 15433625]\) \(72268906496/606436875\) \(-110523120468750000\) \([2]\) \(55296\) \(1.9517\) \(\Gamma_0(N)\)-optimal
9900.e3 9900l2 \([0, 0, 0, -710175, 212111750]\) \(13584145739344/1195803675\) \(3486963516300000000\) \([2]\) \(110592\) \(2.2983\)  
9900.e2 9900l3 \([0, 0, 0, -3514800, 2538300125]\) \(-26348629355659264/24169921875\) \(-4404968261718750000\) \([2]\) \(165888\) \(2.5010\)  
9900.e1 9900l4 \([0, 0, 0, -56249175, 162376190750]\) \(6749703004355978704/5671875\) \(16539187500000000\) \([2]\) \(331776\) \(2.8476\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9900l have rank \(1\).

Complex multiplication

The elliptic curves in class 9900l do not have complex multiplication.

Modular form 9900.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.