Properties

Label 222180.s
Number of curves $2$
Conductor $222180$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 222180.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.s1 222180d2 \([0, 1, 0, -2660, 52308]\) \(-15375747664/128625\) \(-17418912000\) \([]\) \(217728\) \(0.79122\)  
222180.s2 222180d1 \([0, 1, 0, 100, 420]\) \(808496/945\) \(-127975680\) \([]\) \(72576\) \(0.24191\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 222180.s have rank \(1\).

Complex multiplication

The elliptic curves in class 222180.s do not have complex multiplication.

Modular form 222180.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} - 3 q^{11} + 5 q^{13} + q^{15} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.