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Properties

Label 355570.l
Number of curves $3$
Conductor $355570$
CM no
Rank $0$
Graph

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

Elliptic curves in class 355570.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355570.l1 355570l1 \([1, 1, 0, -51433, -4511217]\) \(-16954786009/370\) \(-328376361970\) \([]\) \(1078920\) \(1.3258\) \(\Gamma_0(N)\)-optimal
355570.l2 355570l2 \([1, 1, 0, -17798, -10249348]\) \(-702595369/50653000\) \(-44954723953693000\) \([]\) \(3236760\) \(1.8751\)  
355570.l3 355570l3 \([1, 1, 0, 159987, 274668893]\) \(510273943271/37000000000\) \(-32837636197000000000\) \([]\) \(9710280\) \(2.4244\)  

Rank

sage: E.rank()
 

The elliptic curves in class 355570.l have rank \(0\).

Complex multiplication

The elliptic curves in class 355570.l do not have complex multiplication.

Modular form 355570.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} - 2 q^{15} + q^{16} - 3 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.