Properties

Label 158400.jk
Number of curves $2$
Conductor $158400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jk1")
 
E.isogeny_class()
 

Elliptic curves in class 158400.jk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.jk1 158400me1 \([0, 0, 0, -14700, -1874000]\) \(-117649/440\) \(-1313832960000000\) \([]\) \(552960\) \(1.5866\) \(\Gamma_0(N)\)-optimal
158400.jk2 158400me2 \([0, 0, 0, 129300, 44494000]\) \(80062991/332750\) \(-993586176000000000\) \([]\) \(1658880\) \(2.1359\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158400.jk have rank \(0\).

Complex multiplication

The elliptic curves in class 158400.jk do not have complex multiplication.

Modular form 158400.2.a.jk

sage: E.q_eigenform(10)
 
\(q + q^{7} - q^{11} + 2 q^{13} - 3 q^{17} + q^{19} + O(q^{20})\) 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.