Properties

Label 14700s
Number of curves $2$
Conductor $14700$
CM no
Rank $0$
Graph

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

Elliptic curves in class 14700s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14700.g1 14700s1 \([0, -1, 0, -32258, -2367063]\) \(-3155449600/250047\) \(-294177795030000\) \([]\) \(62208\) \(1.5232\) \(\Gamma_0(N)\)-optimal
14700.g2 14700s2 \([0, -1, 0, 188242, -999963]\) \(627021958400/363182463\) \(-427280535894870000\) \([]\) \(186624\) \(2.0725\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14700s have rank \(0\).

Complex multiplication

The elliptic curves in class 14700s do not have complex multiplication.

Modular form 14700.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 3 q^{11} + 4 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.