Properties

Label 55770l
Number of curves $4$
Conductor $55770$
CM no
Rank $0$
Graph

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

Elliptic curves in class 55770l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55770.s3 55770l1 \([1, 1, 0, -11157, -332691]\) \(31824875809/8785920\) \(42407957729280\) \([2]\) \(193536\) \(1.3223\) \(\Gamma_0(N)\)-optimal
55770.s2 55770l2 \([1, 1, 0, -65237, 6124461]\) \(6361447449889/294465600\) \(1421329208270400\) \([2, 2]\) \(387072\) \(1.6689\)  
55770.s4 55770l3 \([1, 1, 0, 36163, 23544981]\) \(1083523132511/50179392120\) \(-242206341499345080\) \([2]\) \(774144\) \(2.0155\)  
55770.s1 55770l4 \([1, 1, 0, -1031917, 403043269]\) \(25176685646263969/57915000\) \(279544643235000\) \([2]\) \(774144\) \(2.0155\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55770l have rank \(0\).

Complex multiplication

The elliptic curves in class 55770l do not have complex multiplication.

Modular form 55770.2.a.l

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