Properties

Label 111600.s
Number of curves $2$
Conductor $111600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 111600.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111600.s1 111600cl2 \([0, 0, 0, -173475, 59609250]\) \(-458314011/953312\) \(-1200898566144000000\) \([]\) \(1866240\) \(2.1583\)  
111600.s2 111600cl1 \([0, 0, 0, 18525, -1766750]\) \(406869021/1015808\) \(-1755316224000000\) \([]\) \(622080\) \(1.6089\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 111600.s have rank \(0\).

Complex multiplication

The elliptic curves in class 111600.s do not have complex multiplication.

Modular form 111600.2.a.s

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 3 q^{11} - 5 q^{13} + 3 q^{17} + 7 q^{19} + O(q^{20})\) 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 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.